UC-NRLF 


Examination  Manuals 


No.   I. 


Irving  Stringham 


|| 


WENTWOKTH  &  HILL'S 


EXAMINATION  MANUALS, 


No.  I. 


ARITHMETIC. 


BOSTON: 
GINN,   HEATH,    &  COMPANY. 

1884. 


Entered,  according  to  Act  of  Congress,  in  the  year  1883, 

BY  GEORGE  A.  WENTWORTH  AND  GEORGE  A.  HILL, 

In  the  Office  of  the  Librarian  of  Congress  at  Washington. 


J.  8.  CUSHING  &  Co.,  PRINTERS,  BOSTON. 


PREFACE. 


THIS  Manual  consists  of  two  parts :  The  first  part  contains 
one  hundred  and  fifty  examination  papers,  the  questions 
for  which  have  been  selected  mainly  from  the  English,  French, 
and  German  collections  of  problems.  These  papers  may  be  divided 
into  three  groups.  The  first  fifty  papers  are  confined  to  the 
Simple  Rules,  Fractions,  and  Weights  and  Measures ;  the  next 
fifty  papers  cover  all  the  subjects  treated  in  ordinary  text-books 
except  the  Metric  System  ;  the  last  fifty  also  include  the  Metric 
System. 

In  each  group  the  earlier  papers  will  be  found  somewhat 
easier  than  the  later  ones.  The  papers  are  intended  to  be  hour 
papers,  but  if  any  of  them  are  thought  to  be  too  long  for  one 
hour,  the  time  may  be  increased,  or  the  length  of  the  paper 
reduced  by  omitting  one  or  more  questions. 

The  second  part  -  of  the  Manual  is  a  collection  of  recent 
examination  papers  actually  set  in  various  American  and  English 
institutions  of  learning. 

The   Manual  may  be  used   in   two  ways. 

First:  To  test  the  learner's  knowledge  in  the  usual  way  by 
means  of  an  examination.  For  this  purpose  the  class  will  come 
to  the  recitation-room  provided  with  the  Manual  and  blank  books, 
and  the  teacher  will  simply  designate  by  number  the  paper  to 
be  worked. 

Secondly :  To  review^  the  subject-matter  of  Arithmetic.  This 
may  be  done  by  assigning  problems  to  be  worked  in  the  class-room, 

800568 


IV  PREFACE. 


or  by  assigning  to  each  pupil  a  paper  with  directions  to  hand  in 
the  solutions,  neatly  worked  out,  at  a  subsequent  recitation. 

The  Manual  will  be  found  especially  useful  in  preparing  for 
written  examinations. 

Answers  to  the  problems  in  the  first  one  hundred  and  fifty 
papers,  bound  separately  in  paper  covers,  can  be  had  by  teachers 
only,  on  application  to  the  publishers. 

G.   A.  WENTWOETH. 
G.   A.   HILL. 


SPECIMEN  PAPER  WORKED  OUT, 


1.    In  674,381  inches  how  many  miles,  furlongs,  rods,  etc.  ? 

12)674381  in. 
3)  56 198  ft.  5  in. 
18732yds.  2ft. 

2 

11)37464  half-yds. 
40)  3405  rds.  4^  yds. 
8)85  fur.  5  rds. 
10  mi.  5  fur. 

10  mi.  5  fur.  5  rds.  4|  yds.  2  ft.    5  in. 
-4ns.  10  mi.  5  fur.  5 rds.    5yds.  Oft.  11  in. 


2,   Find  the  G.C.M.  of  269,178  and  352,002. 

6)269178  352002 
44863  )  58667(1 

44863 
4)13804 

3451)44863(13 
3451 
10353 
10353 

Ans.  6x3451  =  20,706. 

The  common  factor  6  is  first  taken  out  from  both  numbers.  Fit>m 
the  remainder  13,804,  the  factor  4,  which  is  prime  to  44,863,  is  ejected. 
The  resulting  number  3451  is  contained  13  times  in  44,863,  and  there- 
fore the  greatest  common  measure  is  6  x  3451  =  20,706. 


EXAMINATION    MANUAL. 


3    Simplify 
mPilty 


-- 

3   11   W   396 

12 

1  _2_   7  _  _7_  =  264  +  144  +  231  -  14 
3  11   24  396        792 

iofA  =  _2_;   1-ofl^JL.   Irfl.i. 

3   11  33    11   ££   132    24   3  72 

12 

l_J±__l__jL  =  792  -  48  -  42  -  77  =  625  . 
33  132  72       792       792' 
625  .  625  -  A   l 

792  •"792""1' 

4,  Divide  0.025  by  500,  and  0.03625  by  0.29. 

0.125 

500)0.02500  29)3.625 

0.00005  29_ 

72 
58_ 

145  0.00005  \      A 

145  0.125      j  ' 

5,  Make  out  the  following  bill  : 

3J  pounds  of  tea  at  64  cents  per  pound  ; 
1£  pounds  of  coffee  at  40  cents  per  pound  ; 
62-  pounds  of  loaf  sugar  at  10  cents  per  pound  ; 
H  pounds  of  butter  at  34  cents  per  pound. 
How  much  change  out  of  $5  should  Mr.  Smith  receive? 

Mr.  JOHN  SMITH, 

Dr.  to  JAMES  HORN. 
1883. 

Aug.  17.  Silbs.  of  tea  @  64  cts.  .  .  .  $2.08 
li-  Ibs.  of  coffee  @  40  cts.  ...  .60 
6|  Ibs.  of  sugar  @  10  cts  .....  65  • 

1|  Ibs.  of  butter  @  34  cts.      .     .     .  _  .51 

$3.84 

Received  payment, 
Ans.  $5.00  -$3.84  =  $1.16.  JAMES  HOEN. 


ARITHMETIC.  vii 


6.  If  18  men  can  dig  a  trench  200  yards  long,  3  yards  wide, 
and  2  yards  deep,  in  6  days  of  10  hours  each,  in  how 
many  days  of  8  hours  each  will  10  men  dig  a  trench 
100  yards  long,  4  yards  wide,  and  3  yards  deep  ? 


Men, 

10:     18: 

:  6  days. 

Length, 

200  :  100 

Width, 

3:       4 

Depth, 

2:       3 

Hours, 

8:     10 

9 

2 

3 

JLfi  X  W 

iX^X^Xj 

0  X  ft  _  27  _ 

13J. 

ra  v-  5 

ina  y  2  y  '>  \ 

s   C                     0 

2  2  .Ans.  13J  days. 

7,  What  alteration  will  be  made  in  an  income  by  selling 

$10,000  of  4  per  cent  stock  at  89J,  and  buying  5  per 
cent  stock  at  105  ? 

Income  from  4  per  cent  stock  =  0.04  of  $  10,000    =  $400. 
Proceeds  of  4  per  cent  stock    =  0.89J  of  $  10,000  =  $  8925. 
$1  of  5  per  cent  stock  costs  $1.05  ;  therefore, 
Amount  of  5  per  cent  stock     =  $  8925  H-  1 .05        =  $  8500. 
Income  from  5  per  cent  stock  =  0.05  of  $8500       =  $425. 
•     Increase  in  income  =$425  — $400        =$25. 

8,  A  room  measures  16  feet  by  21  feet,  and  is  11  feet  high. 

There  is  one  door  7  feet  by  3  feet,  and  two  windows 
8  feet  by  4  feet.  Find  the  cost  of  papering  it  with 
paper  2  feet  wide  at  5  cents  a  yard. 

Distance  round  the  room     =16  +  16  +  21  +  21     =74  ft. 
Area  of  walls  of  room          =  11  x  74  =  814  sq.  ft. 

Area  of  door  and  windows  =  21  sq.ft. +64  sq.ft.  =  85  sq.ft. 
Area  to  be  papered  =  814  sq.  ft.  -  85  sq.  ft.  =  729  sq.  ft. 

Area  of  one  yard  of  paper  =3x2  =      6  sq.  ft. 

Number  of  yards  required  =  729  -=-6  =  121  \. 

Cost  of  the  paper  =  121-J  x  $0.05  =  $6.07£. 

Am.  $6.07LV. 


Vlll 


EXAMINATION    MANUAL. 


9,  A  jar  full  of  water  weighs  1.325kg ;  filled  with  mercury 
it  weighs  12.540kg.  What  is  the  capacity  of  the  jar, 
and  its  weight  ?  The  specific  gravity  of  the  mercury 
is  13.59. 


12.540 
1.325 
11.215k8 


13.59 

1 
12.59*8 


0.890781. 
12.59)11.215 
10072 


11430 

11331 
9900 
8815 


10870 


Mercury  in  jar  weighs  11.215k«  more  than  water  in  jar. 

A  liter  of  mercury  weighs  12.59ks  more  than  a  liter  of  water. 


Capacity  of  jar 


11.215 


of  a  liter  -  0.890781. 


12.59 

Weight  of  water  in  jar  =  0.89078k«. 
Weight  of  jar  =  1.325ks  -  0.89078ks  =  0.43422ks  =  434.22s. 

Ans.  0.890781 ;  434.22*. 


10,    Extract  the  cube  root  of  5  to  five  places  of  decimals. 

5.000(1.70997 


3  x  102  = 

3(10x7)  = 

/      == 


300 
210 

559 
259 


3  x  17002  =  8670000 

3(1700x9)=     45900 

92  =  81 


8715981 

45981 

3  X  17092  -  8762043 


4000 


3913 


87  000  000 


78  443  829 


8  556  171  0 
7  885  838  7 


670  332  30 
613  343  01 


1. 709.97  ~Ans. 

For  explanation  of  the  method,  see  Wentworth  and  Hill's  Prac- 
tical Arithmetic,  page  282. 


EXAMINATION  MANUAL. 
ARITHMETIC. 


1. 

1,  Write  in  words  15,006,021,  and  state  how  many  times  a 

number  is  increased  by  annexing  three  ciphers  to  it. 

2,  Multiply  2,035,674  by  3096. 

3,  Divide  275,487  by  736,  and  prove  that  the  result  is  cor- 

rect. 

4,  How  many  times  is  195  yards  1  foot  8  inches  contained 

in  a  mile? 

5,  Find  the   number   of  cubic  inches  in  1  cubic  yard  24 

cubic  feet  760  cubic  inches. 

6,  How  many  grains  of  gold  in  a  cup  weighing  8  ounces 

4  pennyweights  ? 

2. 

1,  How  much  must  be  added  to  sixty  million  four  hun- 

dred six  •  thousand   two   hundred   ninety  to  make 
three  hundred  twenty  million? 

2,  Multiply  456,978  by  789. 

3,  Divide  three  hundred  thirty-seven  million  one  hundred 

three  thousand  twenty-five  by  eight  hundred  sixty- 
one. 

4,  In  674,381  inches  how  many  miles,  rods,  feet,  and  inches? 

5,  Find  the  difference  between  30  years  8  months  3  weeks 

6  days  and  44  years  3  months  1  week  5  days. 


EXAMINATION    MANUAL. 


3. 

1,  Write  in  words  the  sum  of  4,300,702 ;  6,070,506 ;  and 

341,318. 

2,  Find  the  number  which,  subtracted  from  80,000,  leaves 

57,735. 

3,  From  the  sum  of  eight  million  seventy-nine  thousand 

six  hundred  ninety,  and  three  hundred  eighty-five 
thousand  seven  hundred  nine,  subtract  their  differ- 
ence. 

4,  Divide  19,094,867  by  4009. 

5,  The  circuit  of  a  race-course  is  137^  yards.     How  many 

times  must  a  bicyclist  go  round  to  complete  5 
miles  ? 

6,  Take  156  miles  160  rods  216  yards  from  191  miles  80 

rods  2  yards. 

4. 

1,  Write  in  figures  two  million  twenty  thousand  eighty- 

seven. 

2,  Express  in  words  and  in  figures  the  excess  of  the  value 

of  one  5  over  the  other  in  the  number  658,457. 

3,  Multiply  seventeen  thousand  nine  hundred  forty-three 

by  five  thousand  seventy-nine. 

4,  Divide  five  hundred  one  million  five  hundred  by  three 

thousand  eight  hundred  fifty. 

5,  Reduce  125  square  rods  23  square  yards  6  square  feet 

108  square  inches  to  square  yards. 

6,  How  many  grains  in  a  pound  Avoirdupois  ?  in  a  pound 

Troy? 


ARITHMETIC. 


5. 

1,  Write  .in  figures  ten  million  eighty-three  thousand  six 

hundred  eighty. 

2,  Divide  the  product  of  37,800  and  7950  by  630. 

3,  What  number  multiplied  by  6702  will  give  218,773,386? 

4,  How  often  is  £1  17s.  6cZ.  contained  in  £28  2s.  6cZ.? 

5,  An  engine  draws  a  train  of  23  cars,  each  containing  5 

long  tons,  2123  pounds  of  coal.  What  is  the  weight 
of  coal  in  the  train  ? 

6,  A  square   drill-yard  required   869  square   slabs,   each 

measuring  3  square  feet  86  square  inches.  What  is 
the  area  of  the  yard  in  square  feet,  etc.  ? 

7,  Eequired  the  weight  of  a  guinea,  if  45  can  be  coined 

from  a  pound  of  gold. 

6. 

1,  A  person  walked   136  miles  in  40  hours  48  minutes. 

How  many  minutes  was  he  in  walking  a  mile  ? 

2,  How  many  times  must  we  take  the  number  7  to  make 

819? 

3,  By  how  much   does  the  thirty-seventh  part  of  three 

thousand  six  hundred  sixty- three  fall  short  of  a 
hundred  ? 

4,  Reduce  7,896,432  grains  Troy  to  pounds. 

5,  If  56  acres  of  land  cost  $700,  what  will  be  the  value  of 

13  acres  80  square  rods? 

6,  A  man  agreed  to  buy  a  haystack,  paying  $  30  for  each 

load.  He  found  his  wagon  held  1  ton  392  pounds, 
and  that  the  whole  stack  weighed  10  tons  1288 
pounds.  How  much  has  he  to  pay  ? 


EXAMINATION   MANUAL. 


7. 

1,  Find  the  circumference  of  a  carriage  wheel  which  re- 

volves 1848  times  in  a  journey  of  3£  miles. 

2,  In  120,505  square  feet  how  many  acres,  etc.  ? 

3,  If  the  moon  moves  forward  in  her  orbit  57°  13'  18"  in 

13  days,  find  the  distance  she  averages  a  day. 

4,  A  man  can  buy  a  white  hat,  which  lasts  4  months,  for 

§0.75 ;  he  can  buy  a  black  hat,  which  lasts  9  months, 
for  $1.75.  Which  is  the  cheaper?  What  is  saved 
in  3  years  by  wearing  the  cheaper  hat  ? 

5,  Find  the  number  of  pounds  Troy  equal  to  78  pounds  4 

ounces  Avoirdupois. 

6,  Reduce  1  acre  91  square  rods  2  square  yards  to  square 

inches. 

8. 

1,  Reduce  100,196,196  square  inches  to  acres,  etc. 

2,  Reduce  40  pounds  8  ounces  5  drams  1  scruple  7  grains  to 

grains,  Apothecaries'  weight. 

3,  Find  the  cost  of  half  an  acre  of  ground  at  63  cents  per 

square  yard. 

4,  The  distance  between  two  towns  is  18  miles  40  rods  44 

yards.  How  many  telegraph  poles  will  be  required 
between  them,  the  poles  being  8  rods  apart  ? 

5,  If  $328  equal  £74  2s.  I0d.,  by  how  many  pence  does  a 

dollar  exceed  4  shillings  ? 

6,  How  many  cubic  yards,  feet,  and  inches  in  175,983  cubic 

inches  ? 


ARITHMETIC. 


9. 

1,  In  36,845,371  ounces  Avoirdupois,  how  many  long  tons, 

cwts.,  etc.  ? 

2,  In  1,749,134  seconds  how  many  weeks,  days,  etc.  ? 

3,  The  latitude  of  St.  Paul's  in  London  is  51°  30'  49",  and 

that  of  St.  Peter's  in  Home,  41°  53'  54".  What  is 
one-fifth  of  the  difference  of  their  latitudes? 

4,  Reduce  875,679  chains  25  links  to  miles,  rods,  etc. 

5,  Reduce  7658  square  chains  625  square  links  to  acres, 

square  rods,  etc. 

6,  Change  35  pounds  8  ounces  7  pennyweights  17  grains 

Troy  to  Avoirdupois  weight. 

10. 

1,  Express    in    figures   nine   thousand    seventeen    million 

fifty-nine  thousand  ninety-six. 

2,  How  many  days  will  9867  pounds  of  hay  last  13  horses, 

if  each  horse  eats  33  pounds  a  day  ? 

3,  A  boy  has  a  bag  containing  2360  chestnuts ;  he  takes  out 

7  dozen  for  himself,  and  then  divides  the  rest  among 
19  school-fellows,  keeping  those  remaining  over. 
How  many  chestnuts  did  he  then  have,  and  how 
many  did  each  of  the  other  boys  have  ? 

4,  A  city  containing  758,043  inhabitants  has  5  districts. 

The  population  of  the  first  is  78,967 ;  of  the  second, 
139,753;  of  the  third,  145,069;  the  other  two  dis- 
tricts have  each  an  equal  number  of  inhabitants. 
Find  the  population  of  each  of  these  two  districts. 

5,  Reduce  367  acres  155  square  rods  25  square  yards  8 

square  feet  74  square  inches  to  square  inches. 

6,  Reduce  1,186,126  inches  to  miles,  etc. 


EXAMINATION    MANUAL. 


11. 

1,  Reduce  2  miles  3  furlongs  20  rods  1  yard  to  inches. 

2,  What  do  12  dozen  chains  weigh,  if  each  contains  2  ounces 

9  pennyweights  3  grains  of  metal  ? 

3,  Find  the  greatest  common  measure  of  203  and  2291. 

4,  Find  the  least  common  multiple  of  12,  21,  28,  30,  35. 

5,  Multiply  T3T  of  If  by  5J  of  J. 

6,  Add  together  0.0023,  2.38,  250,  0.527. 

7,  Reduce  3  quarts  1  pint  to  the  decimal  of  a  gallon. 

12. 

1,  Reduce  1  furlong  15  rods  1  foot  6  inches  to  yards. 

2,  If  a  person  spends  $2226.50  a  year,  how  much  does  he 

spend  each  day  in  an  ordinary  year  ? 

3,  Find  the  greatest  common  measure  of  2163  and  504. 

4,  Find  the  least  common  multiple  of  18,  16,  63,  24,  56. 

5,  Find  the  value  of  21 X  If  of  l&X  3J  of  1^. 

6,  Subtract  2.03  from  20.2. 

7,  Find  the  value  of  0.625  of  a  gallon. 


ARITHMETIC. 


13. 

1,  Eeduce  357,000  inches  to  miles,  furlongs,  rods,  etc. 

2,  At  a  festival  23,760  persons  entered  the  enclosure  be- 

tween 10  AM.  and  4  P.M.     What  was  the  average 
per  minute  ? 

3,  Find  the  greatest  common  measure  of  5292  and  1520. 

4,  Find  the  least  common  multiple  of  4,  9,  16,  28,  42. 

5,  Divide  5J  by  -|. 

6,  If  I  sell  -f  of  |-  of  an  estate,  what  part  of  the  estate 

have  I  left  ? 

7,  Multiply  3.26  by  1.02. 


14. 

1,  A   dozen  persons   hire    an   omnibus   for  $9.25.     How 

much  more  must  each  pay  than  if  the  party  were 
fifteen  in  number? 

2,  Find  the  greatest  common  measure  of  3575  and  4719. 

3,  Find  the  least  common  multiple  of  6,  15,  18,  35,  72. 

4,  Divide  20T\  by  17TV 

5,  Find  the  value  of  -|  of  an  acre. 

6,  Divide  998.824392  by  0.018. 

7,  Reduce  5  ounces  12  pennyweights  16  grains  to  the  deci- 

mal of  a  pound. 


EXAMINATION    MANUAL. 


15. 

1,  Find  the  greatest  common  measure  of  5292  and  8316. 

2,  Find  the  least  common  multiple  of  8,  12,  18,  24,  27. 

3,  Add  together  £ ,  -J-,  -J. 

4,  Find  the  value  of  -ff^  of  a  bushel. 

5,  Divide  2  weeks  3  days  by  3|. 

6,  Divide  160.68  by  3.9. 

7,  Reduce  3  quarters  3  pounds  2  ounces  2.816  drams  to 

the  decimal  of  a  long  ton. 


16. 


1,  Find  the  greatest  common  measure  of  731,  2329,  and 

3502. 

2,  Find  the  least  common  multiple  of  3,  8,  17,  40,  153. 

3,  Add  if  A,  A- 

4,  Which   is  the  greater  £  of  4  or  J   of  5,  and  by  how 

much? 

5,  Find  the  value  of  21  of  5  bushels  -j-  1J  of  2J  pecks. 

6,  Divide  0.3964  by  0.75. 


ARITHMETIC. 


17. 


1,  Keduce  f  of  a  pound  Troy  to  the  fraction  of  a  pound 

Avoirdupois. 

2,  Divide  52  by  3.2. 

3,  Express  0.305  as  a  common  fraction  in  its  lowest  terms. 

4,  Add  together  2f ,  41,  3T\. 

5,  Find  the  greatest  common  measure  and  least  common 

multiple  of  125,  175,  225. 

6,  Divide  f  of  £  by  f  of  f . 


18. 


1,  Which  is  the  greater  f  of  1|  or  -f  of  5J,  and  by  how 

much? 

2,  Simplify  21  -f  f  of  5|-  +  4T7T  +  5. 

3,  Add  together  -|  and  2f ,  and  subtract  their  sum  from  4. 

4,  Multiply  0.026  by  3,3  ;  by  0.33;  by  33 ;  and  by  0.033. 

5,  Divide  1.8  by  500. 

6,  Express  0.0075  as  a  common  fraction  in  its  lowest  terms. 


10  EXAMINATION   MANUAL. 

19. 

1,  Add  together  3J  of  1|  and  2f  of  If 

2,  Subtract  I  of  H  from  J  of  2f. 

g3 

3,  Reduce  to  a  simple  fraction  ~. 

**§ 

4,  Divide  611  by  0.13. 

5,  Reduce  7.2  feet  to  the  decimal  of  a  rod. 

6,  Find  the  value  of  0.065  of  an  acre. 

7,  Reduce  -J-|ff  to  its  lowest  terms. 

20. 

1,  Subtract  £  from  f  ;  -f-  from  £  ;  and  $  from  1^  ;  and  add 

together  the  results. 

2,  Multiply  2  yards  1  foot  7^  inches  by  ^-. 

3,  Reduce  -f^  of  a  pint  to  the  fraction  of  a  gallon. 

4,  Divide  2175.68  by  100. 

5,  Reduce  ^ff  to  its  equivalent  decimal  fraction. 


6,  Reduce  15  square  rods  to  the  decimal  of  one-half  an 

acre. 

7,  Find  the  value  of  0.009943  of  a  mile. 


ARITHMETIC.  11 


21. 

1,  Find  the  value  in  English  money  of  1572.4185  francs, 

when  the  exchange  is  at  26.675  francs  per  pound. 

2,  Divide  101  by  1.01,  and  0.101  by  10.1. 

3,  Reduce  14  hours  15  minutes  to  the  fraction  of  3  J  days. 

4,  Reduce  to  a  simple  fraction  ^— J 

o  +  T 

5,  Find  the  greatest  common  measure  and  least  common 

multiple  of  144,  176,  272. 

6,  How  many  plots  of  2 1  acres  each  can  be  made  out  of  an 

estate  one  mile  square  ? 


22. 

L   A  man  steps  2  feet  8  inches  at  each  step.     How  many 
steps  will  he  take  in  2  miles? 

2,  Reduce  to  its  lowest  terms  |j J§. 

3,  Subtract  121|  from  202£. 

4,  How  can  you  determine  that  a  number  is  divisible  by 

3  without  actually  dividing  by  3  ? 

5,  Two  pipes  together  fill  a  cistern  in  1  hour,  and  one  of 

them  alone  fills  it  in  H  hours.     How  long  will  it 
take  the  other  alone  to  fill  it  ? 

6,  Divide  3.52  by  2.2  ;  by  0.22  ;  and  by  22. 


12  EXAMINATION    MANUAL. 

23. 

1,  In  640,825  seconds  how  many  weeks,  days,  etc.  ? 

2,  Reduce  -J-f-fyJ-  to  its  lowest  terms. 

3,  Add  16ft,  1«,  i  A- 

4,  Subtract  3 1  from  30^. 

5,  Find  the  product  of  1-fo  X  3^-f  X  -^  X 


6,  If  T7^-  of  an  estate  be  worth  §3003,  what  is  the  value  of 

the  estate? 

7,  Reduce  213  rods  1  yard  2  feet  6  inches  to  the  common 

fraction  of  a  mile. 


24. 

1,  Divide  0.05625  by  0.0275. 

2,  Reduce  £3  15s.  6.5  d.  to  the  decimal  of  £4. 

3,  Westminster  Hall  is  237  feet  long  by  G8  feet  wide  ; 

Brussels  Town  Hall,  264  feet  by  50  feet.  How 
many  more  persons  could  Westminster  Hall  accom- 
modate than  Brussels  Town  Hall,  allowing  f  of  a 
square  yard  to  each  person? 


4,  Simplify  2^  +  |  X  |-  21 

5,  Multiply  9-3^  by  16}  of  1TV 

6,  Divide  5&  -||  by  If  of  8j. 


ARITHMETIC.  13 


25. 

1,  Find  the  value  of  jJt-^J*L  multiplied  by  •&  of  6. 

^  6~  +  2"  +  -g" 

2,  Reduce  to  its  lowest  terms  J|-f|f. 

3,  A  can  do  a  piece  of  work  in  10  days,  B  can  do  the  work 

in  15  days.     In  what  time  can  they  both  do  it  work- 
ing together  ? 

4,  Arrange  in  order  of  magnitude  2.5  X  0.075;  2.625-^-7; 

5  X  0.05. 

5,  Reduce  0.972  to  its  equivalent  common  fraction. 

6,  Reduce  to  a  decimal  Tf  f -3-. 

7,  Reduce  0.9  of  a  pound  Avoirdupois  to  the  decimal  of  5 

pounds  Troy. 

26. 

1,  How  many  cubic  inches  in  a  brick  that  is  9  inches  long, 

4  inches  wide,  3  inches  thick? 

2,  Reduce  to  a  simple  fraction  3|  X  3T%  X  2f\-  X  2-^-  X  -£5. 

3,  What  fraction  of  J-  of  a  mile  is  1 J  feet  ? 

4,  Reduce  6|-  of  365^  days  to  the  fraction  of  3  years. 

5,  Express  in  figures  seventy-three  ten-thousandths. 

6,  Reduce  0.536  to  a  common  fraction. 

7,  Divide  0.005868  by  0.036,  and  arrange  the  divisor,  divi- 

dend, and  quotient  in  order  of  magnitude. 

8,  Divide  0.5  by  25 ;   87.5  by  2.5 ;  and  0.055757592  by 

0.009207. 


14  EXAMINATION   MANUAL. 


27. 

1,  Divide  10.8528  by  1.02  and  express  the  quotient  as  a 

common  fraction. 

2,  Reduce  2.5  gills  to  the  decimal  fraction  of  3£  gallons. 

3,  Find  the  value  of  14.1275  acres. 

4,  What  is  the  value  of  40  acres  132  square  rods  at  $37.50 

per  acre  ? 

5,  A  railway  train  goes  200  miles  in  8  hours.    In  what  time 

will  it  make  a  journey  of  40  miles  ? 

6,  How  long  will  a  journey  of  15  miles  24  jods  3  yards 

take  at  the  rate  of  3  miles  204  rods  3  yards  in  56 
minutes  ? 

28. 

1,  A  race-horse  goes  5  miles  in  32  minutes.     How  long 

will  he  be  in  going  1650  yards? 

2,  Reduce  -J  of  ^  of  a  mile  to  the  fraction  of  f  of  -jf  of  8 

miles. 

3,  Reduce  5.018  to  its  equivalent  common  fraction. 

4,  Simplify 


5,  Express  2  feet  3  inches  as  the  fraction  of  4£  yards. 

6,  Resolve  18,  16,  36,  44,  45,  48,  63,  121  into  their  sim- 

plest factors,  and  find  their  least  common  multiple. 


ARITHMETIC.  15 


29. 

1,  Sound  travels  at  the  rate  of  1120  feet  in  a  second.    How 

far  off  is  a  thunder  cloud,  when  the  clap  follows 
the  flash  of  lightning  in  10 J  seconds? 

2,  The  four  sides  of  a  field  are  23  chains  19  links,  17  chains 

34  links,  6  chains  85  links,  24  chains  62  links.  How 
many  yards  around  the  field  ? 

3,  Reduce  10,000  square  yards  to  acres,  etc. 

4,  Find  the  sum  of  8  cubic  yards  13  cubic  feet  1234  cubic 

inches,  5  cubic  yards  14  cubic  feet  976  cubic  inches, 
2  cubic  yards  5  cubic  feet  854  cubic  inches,  and  7 
cubic  yards  10  cubic  feet  1012  cubic  inches. 

5,  Express  1  peck  6  quarts  1  pint  as  the  fraction  of  6  bush- 

els 1  peck  3  quarts. 

6,  Express  13  hours  15  minutes  17  seconds  as  the  fraction 

of  6  days  1  hour  48  minutes  7  seconds. 

7,  Find  the  value  of  -fa  of  3  long  tons  5  cwt.  101  pounds. 

30. 

1,  There  are  7  miles  of  road  in  a  certain  district.     If  the 

average  width  of  the  road  is  half  a  chain,  how 
many  acres  of  land  consist  of  roads  ? 

2,  Reduce  1012  quarts  to  bushels. 

3,  Reduce  673,856  seconds  to  days. 

.4.  A  dishonest  milkman  mixes  a  pint  of  water  with  every 
two  quarts  of  milk.  How  many  gallons  will  he 
make  in  this  way  out  of  20  gallons  of  pure  milk  ? 

5,  A  well  is  18  yards  2  inches  deep,  and  the  wheel  is  4  feet 

2  inches  round.  How  many  turns  of  the  wheel  will 
raise  the  bucket  ? 

6,  Express  1  day  1  hour  50  minutes  42  seconds  as  a  decimal 

of  a  day. 

7,  Express  in  days,  hours,  etc.,  the  true  length  of  a  year, 

365.242218  days. 


16  EXAMINATION    MANUAL. 

31. 

1,  Find  the  least  common  multiple  of  8,  10,  12,  25,  30,  36. 

2,  Add  f  of  a  score  to  -f-  of  a  dozen,  and  subtract  from  the 

result  |  of  a  hundred.     What  is  the  remainder  ? 

3,  A  cistern  can  be  filled  in  20  minutes  by  one  pipe  and 

in  30  minutes  by  another.     In  how  many  minutes 
will  it  be  filled  by  both  together  ? 

4,  Express  If  of  7  yards  2  feet  9  inches  as  a  fraction  of 

13  yards  7  inches. 

5,  A  man  walked  111  miles  in  3 \  hours.     How  long  would 

he  be  in  going  20  miles  at  the  same  rate  ? 

6,  Divide  723.6  by  22.5 ;  and  7.236  by  0.0225. 

7,  Find  the  value  of  3.5  X  0.8. 

32. 

1,  Find  the  value  of  0.3  X  0.27. 

2,  If  -|  of  a  ton  of  coal  costs  $4,  what  will  \\  cwt.  cost? 

3,  Find  the  value  of  0.2625  of  a  mile. 

4,  The  highest  mountain  in  the  world  is  Dhawalaghiri,  in 

the  Himalayas,  and  is  28,000  feet  above  the  level  of 
the  sea.  Express  this  as  a  decimal  of  the  earth's 
radius,  4000  miles. 

5,  From  1  pound  Troy  of  standard  gold  are  coined  46.725 

sovereigns.  Find  the  weight  in  grains  of  each  sov- 
ereign. 

6,  The  depth  of  a  canal  is  6  feet  4  inches,  the  width  19  feet 

8  inches,  and  the  length  20  miles.  How  many  cu- 
bic feet  of  water  will  it  hold  ? 


ARITHMETIC.  17 


33. 

1,  Add  together  -^,  -^-,  •£$,  and  -|. 

2,  Divide  -^  by  6|. 

3,  Reduce  789,654,328  inches  to  miles. 

4,  Reduce  £25  16s.  Sd.  to  the  fraction  of  £15  10s. 

5,  The  upper  floor  of  a  house  is  18  feet  4  inches  above 

the  ground  and  is  reached  by  two  equal  staircases, 
separated  by  the  landing  of  the  first  floor.  How 
many  stairs  are  there  in  each  staircase,  if  each  stair 
is  11  inches  high  ? 

6,  How  many  hurdles  will   it  take  each  5£  feet  long  to 

make  a  square  sheep-fold,  each  side  of  which  is  40 
rods? 

7,  If  a  quantity  of  wheat  fills  1155  sacks,  each  holding 

8  bushels  4  quarts,  how  many  sacks  will  it  take  to 
contain  the  wheat  when  each  sack  holds  6  bushels  3 
quarts  ? 

34. 

1,  If  64  gallons  of  wine  and  16  gallons  of  water  are  mixed, 

how  much  wine  is  there  in  2  quarts  1  pint  of  the 
mixture  ? 

2,  Find  the  total  weight  of  5792  iron  bars,  each  weighing 

23  pounds  10  ounces. 

3,  Reduce  0.056  of  a  square  rod  to  the  decimal  of  an  acre. 

4,  Find  the  value  of  0.58  of  a  common  year. 

5,  The  price  of  gold  being  £3  17s.  10 £  d.  an  ounce,  find 

the  weight  of  a  nugget  worth  £341.0925. 

6,  Find  the  greatest  common  measure  and  least  common 

multiple  of  161,  253,  299. 

7,  Simplify  1^-  +  f  of  ^  -  H  of  6±. 


18  EXAMINATION   MANUAL. 

35. 

1.  Add  0.60457;    46.70056;    5.80007;    and  4.7896. 

2,  Divide  5.0666  by  21.56. 

i  3,    Reduce  2.025  miles  to  yards. 

4.  Find  the  difference  between  0.44  of  1  week  and  0.125  of 

8  days. 

5,  If  the  weight  of  1  cubic    foot  of  water  is  62^-f  pounds, 

find  the  error  in  calculating  the  weight  of  1000  cu- 
bic feet,  on  the  assumption  that  1  cubic  foot  weighs 
1000  ounces. 

6.  Supposing  the  quick-step  in  marching  to  be  2  paces  per 

second,  and  the  length  of  each  pace  to  be  28  inches, 
find  the  time  in  which  a  regiment  will  march  35 
miles. 

7,  Simplify  H-(H  of  J). 

36. 

1,  Reduce  186  yards  2  feet  8.04  inches  to  the  decimal  of  a 

chain  (22  yards). 

2,  Add  together  -fa  of  a  square  mile,  y7^  of  an  acre,  and 

-f  of  a  rood,  giving  the  result  in  acres,  roods,  and 
square  rods. 

3,  Simplify  1  +  61  xM-^xJ, 

4,  Reduce  3  cwt.  14  pounds  to  the  decimal  of  a  long  ton. 

5,  Find  the  rent  of  215  acres  45  square  rods  at  $5.62  an 

acre. 

6,  If   4-J  ounces  Avoirdupois   cost   $8|^-,  what  will   Sj-f 

pounds  cost? 


ARITHMETIC.  19 


37; 

1.  If  a  bankrupt  has  assets  to  the  amount  of  $1020,  and 

debts  to  the  amount  of  $3225,  how  many  cents  on  a 
dollar  will  his  creditors  receive  ? 

2.  Two  farmers  bought  a  crop  of  hay.     One  took  -|  of  it, 

and  paid  $  12.     What  had  the  other  to  pay  ? 

3.  In    a   town  of  450  people,  0.44  were  men   and   boys, 

0.38  were  women  and  girls,  and  the  rest  were  chil- 
dren. How  many  were  there  of  each  ? 

4.  If  the  carriage  of  12i  cwt.  for  50  miles  cost  $3^,  what 

will  it  cost  to  carry  17?  cwt.  the  same  distance? 

5.  Simplify  (2 J  +  i)-f-(2f-i). 

6.  If  |  of  a  yard  cost  f  of  $1,  what  will  ||  yards  cost? 

7.  Divide  7.584057  by  11.7. 

38. 

1.  In  4,076,412  dwts.  Troy,  how  many  pounds,  ounces,  etc.  ? 

2.  Divide  lOOf  by  35. 

3.  Divide  18,454.9239  by  0.1225. 

4.  In  17,630,754  square  inches,  how  many  acres,  etc.? 

5.  Subtract  8^  from  12^. 

6.  Subtract  6.04083  from  12.7. 

7.  A  person  sold  •§  of  his  estate,  bequeaths  f  of  the  re- 

mainder to  his  son,  and  leaves  the  rest  to  be  dis- 
tributed equally  among  3  charities.  If  each  of 
these  charities  receives  $136.25,  what  is  the  value 
of  the  estate? 


20  EXAMINATION   MANUAL. 

39. 

1.  Find  the  value  of  -ff  of  a  mile. 

2.  Keduce  2  weeks  2  days  19£  hours  to  the  fraction  of  a 

month  (4  weeks). 

3..    Reduce  y5¥9Q-  to  a  decimal. 

4.  A  bankrupt's  liabilities  are  £3768  17s.  6  d.     "What  are 

his  assets,  if  he  can  pay  13  s.  7?  d.  in  the  pound  ? 

5.  Subtract   -f-%   dwt.  from  2.6  ounces,  and  give  the   an- 

swer as  the  decimal  of  a  pound  Troy. 

6.  Divide  218.4  by  0.168. 

7.  Divide  12  by 


40. 

1.  Express  13  minutes  7£  seconds  as  the  decimal  of  1  hour. 

2.  Add  6,  l\,  ^,  and  ft. 

3.  Find  the  cost  of  11  miles  120  rods  165  feet  of  railway 

at  §32,500  per  mile. 

4.  Add  2.6  days  and  0.85  of  an  hour,  and  give  the  an- 

swer in  minutes. 

5.  In  156,704  square  inches,  how  many  square  yards,  etc.? 

6.  Divide  8.4605  by  0.248  to  three  places  of  decimals. 

7.  Subtract  6f  from  Sf 


ARITHMETIC.  21 


41. 

1.  In  57,625,318  square  inches,  how  many  acres,  square 

rods,  etc.  ? 

2.  A  bankrupt's  estate  amounts   to   £910  3s.  Hd,  and 

his  debts  to  £875.  How  much  can  he  pay  in  the 
pound  ? 

3.  -What  is  the  circumference  of  a  wheel  which  makes  514 

revolutions  in  passing  over  1  mile  467  yards  1  foot? 

4.  Find  the  value  of  5f  —  4f  +  -f-^—  If 

5.  From  21-J-31  take -i-Xf  X-f-Xf. 

6.  Divide  18.13  by  0.00037. 

42. 

1.  A  piece  of  cloth,  when  measured  with  a  yard  measure 

that  is  -f  of  an  inch  short,  appears  to  be  10  £  yards 
long.  What  is  its  true  length  ? 

2.  Divide  120,987.2  by  400. 

3.  Add  |f  3-J-,  1/T,  and  -fr. 

4.  Simplify 

y  A  -4y  A  U^ 

5.  The  weight  of  a  cubic  inch  of  water  is  253.17  grains ; 

that  of  a  cubic  inch  of  air  0.31  grains.  Find  to  three 
places  of  decimals  how  many  cubic  inches  of  water 
are  equal  in  weight  to  1  cubic  foot  of  air. 

6.  Find  the  price  of  5  acres    72  square  rods  of  land  at 

$47.50  per  acre. 


22  EXAMINATION    MANUAL. 

43. 

1.  Reduce  42  rods  1  yard  8  inches  to  the  fraction  of  a  mile. 

2.  Find  the  value  of  1.46875  acres. 

3.  Divide  the  product  of  6.225  and  8.25  by  0.0025. 

4.  What  fraction  multiplied  by  f  will  give  f  ?  what  frac- 

tion divided  by  f  will  give  -|  ?  what  fraction  sub- 
tracted from  -^-  will  give 

5.  Arrange  in  order  of  magnitude 

6.  A  and  B  start  at  a  distance  of  64  miles  from  each  other. 

A  walks  3J  miles  an  hour ;  B,  2£.  If  they  start  at 
the  same  time,  how  many  miles  will  they  each  walk 
before  they  meet  ? 

7.  A  ship  left  England  at  noon,  January  1,  1851.     She 

reached  a  port  in  Australia  at  midnight  (Greenwich 
time),  April  23.  If  the  length  of  the  voyage  was 
18,225  miles,  what  was  her  average  rate  per  hour  ? 

44. 

1.  Subtract  17.2398  from  27.06. 

2.  Multiply  46.2375  by  0.0074. 

3.  Divide  92.3784  by  0.623  to  three  places  of  decimals. 

4.  Find  the  product  of  T\,  ^,  9f ,  and  2f 

5.  Subtract  4.42  of  an  hour  from  3.64  of  a  day. 

6.  Reduce  136,240  square  feet  to  acres,  etc. 

7.  Reduce  234,567  grains  to  pounds,  ounces,  etc.,  Apothe- 

caries' weight. 


ARITHMETIC.  23 


45.. 

1.  The  imperial  gallon  contains  277.274  cubic  inches.  What 

is  the  size  of  a  pint  pot  in  cubic  inches  ?  What  Aveight 
of  water  will  it  hold,  if  a  cubic  foot  of  water  weighs 
1000  ounces? 

2.  What  number  added  to  the  sum  of  -f ,  f ,  f,  and  f  will 

make  4? 

3.  A  field  of  3  J  acres  is  divided  into  28  equal  parts.    What 

fraction  of  an  acre  is  there  in  each  part  ? 

4.  Find  the  sum  of  17.01,  0.1303,  500.42101,  0.001,  and 

6.6. 

5.  Divide  6.2301533682  by  8.8964. 

6.  If  7  tons  336  pounds  of  coal  cost  $32.50,  what  will  1232 

pounds  cost? 

46. 

1.  Find  the  wages  of  a  man  for  3  weeks  4  days  8  hours  at 

$8  per  week,  reckoning  6  days  to  a  week  and  10 
hours  to  a  day. 

2.  Eeduce  30  rods  2  yards  1  foot  to  the  fraction  of  150 

rods  4  yards  2  feet  1  inch. 

3.  If  f  of  an  estate  is  worth  $870,  what  is  the  value  o 

of  it? 

4.  Express  in  the  simplest  form  3-|  +  -J  of 

T8 

5.  What  number  multiplied  by  ^  will  produce  90J  ? 

6.  What  number  added  to  lI7-5-  +  3^- +  2^- + -js¥  will  make 

the  sum  total  10  ? 

7.  Give  in  feet  the  value  of  7.0125  miles. 


24  EXAMINATION   MANUAL. 

47. 

1.  Given  the  fractions  -g%,  T3/T,  and  -^¥7¥;  express  the  differ- 

ence of  the  first  two  as  a  fraction  of  the  difference 
of  the  last  two. 

2.  Reduce  ]|||  to  its  lowest  terms. 

3.  Divide  16.9  by  0.0013,  and  also  by  1.3. 

4.  Reduce  0.53  and  0.00987  to  equivalent  common  frac- 

tions. 

5.  Find  the  value  of  0.3925  of  2  years,  each  year  contain- 

ing 365i  days. 

6.  Reduce  6  yards  2  feet  7.5  inches  to  the  decimal  of  a  mile. 

48. 

1.  What  decimal  of  1  day  is  23  hours  15  minutes  6  seconds? 

2.  Find  the  average  of  21f  ,  73£  ,  0,  3^,  82,  17^,  H» 


3.  Add  ^  of  £5,  $  of  £9  13  s.  2|  d.,  and  -^  of  2s.  6d. 

4.  A  and  B  can  do  a  piece  of  work  in  7  days,  B  and  C  can 

do  the  work  in  8  days,  and  all  three  together  can  do 
it  in  5  days.  What  part  of  the  whole  work  can  each 
do  in  1  day  ? 

5.  What  will  be  the  cost,  at  18  cents  a  square  yard,  of  paint- 

ing the  walls  of  a  room  17  feet  3  inches  long,  15 
feet  5  inches  wide,  and  13  feet  6  inches  high,  allow- 
ing 54  square  feet  for  windows,  etc.  ? 

6.  Find  what  fraction  the  sum  of  -^  £$,  -jV>  anc^  IT  *s  °f 

2^  of  1|  of  f 


ARITHMETIC.  25 


49. 

1.  A  person  possessing  -^  of  an  estate  sold  y  of  y^-  of  his 

share  for  $120.62*.     What  would  -J-  of  T8T  of  the 
whole  estate  sell  for  at  the  same  rate  ? 

2.  Express  as  a  fraction  of  $5  the  difference  between  $7|- 

andf  of  $7. 

3.  Subtract  2.63  dwts.  from  12.13  ounces  Troy,  and  express 

the  answer  in  pennyweights.   " 

4.  In  76,128,976  inches  how  many  miles,  etc.? 

5.  Divide  78  by  361.059  to  three  places  of  decimals. 

6.  Find  the  value  of  2.5 +  —  - 6.002. 


50. 

1.    Find  the  average  of  12Jf ,  21,  7f ,  0.034,  3.125,  0,  24.5, 
and  12^.     Express  the  fractional  part  decimally. 

435.1x0.0046 


2.    Reduce  to  the  simplest  form 


0.125 


3.  Divide  the  sum  of  14.4  and  1.44  by  their  difference, 

and  express  the  result  as  a  common  fraction. 

4.  A  can  build  a  wall  in  3i  days,  and  B  in  5  J  days.  In  what 

time  will  A  and  B  together  do  it? 

5.  A  brick  9  inches  long,  4J  inches  broad,  and  3  inches 

thick  weighs  9  pounds  nearly.  What  would  a  brick 
weigh  if  it  were  12  inches  long,  6  inches  broad,  and 
4  J  inches  thick  ? 

6.  Subtract  73.4698  from  108.30125. 


26  EXAMINATION   MANUAL. 


51. 

1.  Add  £,  2-f ,  and  13T% ;  divide  this  sum  by  13^ ;  and 

subtract  the  result  from  5T3Q-. 

2.  A  cistern  can  be  filled  in  50  minutes  by  one  pipe,  and  in 

1  hour  5  minutes  by  another.  In  how  many  minutes 
will  it  be  filled,  if  both  are  open  together? 

3.  If  a  4  per  cent  stock  is  at  82|,  what  will  be  the  cost  of 

$1000  stock,  and  what  sum  will  be  gained  by  sell- 
ing out  at  86i  ? 

4.  An  army  is  besieging  a  town  in  which  are  1000  men, 

with  provisions  for  three  months.     HowT  many  must 
.  leave  at  once,  in  order  that  the  rest  may  be  able  to 
subsist  a  year  ? 

5.  Divide  7.619  by  0.0019. 

6.  Arrange  in  order  of  magnitude  ^  -fj,  -J-J,  ^. 

52. 

1.  A  room  is  20  feet  6  inches  long,  15  feet  6  inches  wide, 

and  16  feet  high.  It  has  two  doors,  each  8  feet  by  3 
feet  9  inches  ;  it  has  one  window  5  feet  by  7  feet,  and 
two  windows,  each  5  feet  by  4  feet.  What  will  it 
cost  to  paper  the  room  with  paper  1  yard  wide,  at 
20  cents  per  yard  ? 

2.  Divide  0.101  by  0.5;  by  0.05;  by  50;  and  by  5000. 

3.  Eeduce  to  a  common  fraction  0.01034. 

4.  Divide  A  of  #  by  T%  of  -ftf 

5.  Find  the  square  root  of  488,601. 

6.  Find  the  simple  interest  of  $1025  for  13  years  at  43  per 

cent. 


ARITHMETIC.  27 


53. 

1.  If  -f  of  a  yard  of  cloth  cost  -|  -of  a  dollar,  what  will 

-j^-  of  a  yard  cost? 

2.  Find  the  greatest  common  measure  of  2526  and  2947. 

3.  Subtract  0.002  from  11,  and  multiply  0.01  by  1.01. 

4.  Divide  2f  of  If  by  3£  of  f  of  £. 

5.  If  0.5  of  £1  buys  0.4  of  a  gallon,  how  much  may  be 

bought  for  6s.  3d? 

6.  A  steam  engine  and  a  horse  start  together.    The  engine 

does  the  first  mile  in  5  minutes,  the  horse  in  4  min- 
utes. After  this  mile  the  rate  of  the  engine  is  30 
miles  per  hour,  that  of  the  horse  20  miles  per  hour. 
Which  wins  in  a  three-mile  race,  and  by  how  much? 

54. 

1.  Divide  1.44  by  1.2  ;  by  12  ;  by  0.012  ;  and  by  120. 

2.  Find  the  square  root  of  449.44. 

3.  What  is  the  cost  of  carpeting  a  room  21  feet  by  30  feet 

with  carpet  half  a  yard  wide,  running  across  the 
room,  at  75  cents  a  yard  ? 

4.  Divide  §1300  into  three  parts,  in  the  ratio  of  6,  4,  3. 

5.  If   12  men  do  a  piece  of  work  in  15  days  of  12  hours 

each,  how  many  days  of  9  hours  will  10  men  take  to 
do  it? 

6.  Find  the  income  produced  by  investing  $4500  in  3  per 

cent  bonds  at  90 ;  and  that  produced  by  investing 
$2850  in  3J  per  cent  bonds  at  95. 


28  EXAMINATION    MANUAL. 

55. 

1.  Reduce  12  s.  6  d.  to  the  decimal  of  a  pound  sterling. 

2.  Divide  -J  of  £  of  4f  of  2J-  by  £  of  4-J-  of  3|  of  If 

3.  Find  the   compound  interest  on  $100  for  two  years  at 

10  per  cent. 

4.  If  24  men  do  a  piece  of  work  in  14  days  of  9  hours,  how 

many  men  will  do  it  in  12  days  of  7  hours. 

5.  Find  the  least  common  multiple  of  10,  14,  15,  21,  30,  42. 

6.  What  sum  invested  in  3  per  cent  bonds  at  92  will  pro- 

duce an  income  of  $  100  per  annum  ? 

7.  The  gross  receipts  of  a  railway  company  are  $231,100. 

After  deducting  35  per  cent  for  working  expenses, 
and  paying  6  per  cent  interest  on  $2,500,000  bonds, 
what  sum  is  left  for  dividing  among  the  share- 
holders ? 

56. 

1.    Express  as  a  decimal  fraction  the  sum  of  -|,  J,  -|,  J,  T9-^, 


2.    Simplify  _  _;  and 

O     I          6  - 


3.  Divide  36.33  by  210  ;  35  by  0.05  ;  0.002  by  200. 

4.  Find  the  square  root  of  22.1841. 

5.  If  3  pounds  of  tea  at  $1.56  per  pound,  5  pounds  at 

$1.20,  and  7  pounds  at  $.60  are  mixed,  at  what 
price  per  pound  must  the  mixture  be  sold  to  gain  2  £ 
per  cent? 

6.  Find  the  interest  of  $  535  for  9  months  at  41  per  cent. 


ARITHMETIC.  29 


57. 

1,  Find   the    greatest    common   measure    of   124,321    and 

197,451. 

2,  Reduce  0.075  of  a  pound  sterling  to  the  common  frac- 

tion of  4  s.  6  d. ;  and  2  square  rods  9  square  yards  4 
square  feet  72  square  inches  to  the  common  fraction 
of  1  acre  60  square  yards. 

3,  A  man  buys  eggs  at  11  cents  per  dozen,  and  sells  them 

at  2  cents  apiece.     What  does  he  gain  per  cent  ? 

4,  What  sum,  if  put  out  at  3&  per  cent  for  6  years,  will 

produce  $28.87i-,  simple  interest? 

5,  Divide  1.69  by  0.13  ;  12.1  by  0.011 ;  0.001  by  0.01. 

6,  Find  the  square  root  of  4.1209. 

58. 

1,  Find   the   simple    interest   on   $387.50   for  5   years   3 

months  at  3£  per  cent. 

2,  Find  the  least  common  multiple  of  3,  5,  7,  9,  15,  63. 

3,  Divide  l-a  +  i  +  ^)  by  1-Jof  1  of  ^. 

4,  Multiply  0.000725  by  31.25  ;   and   divide  the  product 

successively  by  6.25,  625,  and  0.0625. 

5,  At  what  price  per  hundredweight  must  goods  be  sold, 

which  were  bought  at  $5  per  ton,  in  order  to  gain 
6  per  cent  ? 

6,  A  manufacturer  makes  a  profit  of  20  per  cent,  whole- 

sale dealer  25  per  cent,  shopkeeper  40  per  cent. 
What  is  the  first  cost  of  an  article  bought  at  a  shop 
for  $4.20? 


30  EXAMINATION    MANUAL. 

59. 

1,  Divide  $  154  among  4  persons  in  the  proportion  of  £, 

i  i  i 

2,  In  how  many  days  of  12  hours  will  72  men  do  a  piece 

of  work   which   60   men    can  do  in  30  days  of  9 
hours  ? 

3,  Find  the  interest  on  $354.27  for  3  years  2  months  12 

days  at  2i  per  cent. 

4,  $4500  is  divided  among  A,  B,  C,  and  D.     A  receives 

i  of  the  money,  B  and  C  each  f  of  the  remainder. 
How  much  is  left  for  D  ? 

5,  Express  as  common  fractions  0.001375  ;    0.03  ;  7.19318. 

6,  A  can  walk  10  miles  in  2i  hours,  and  B  can  walk  11 

miles  in  2 \  hours.     They  start  to  walk  a  match  of 
55  miles.     Which  will  win,  and  by  how  much  time  ? 

60. 

1,  The  profit  made  by  selling  beer  at  1  d.  per  pint  above 

cost  is  50  per  cent.      What  is  the  gain  per  cent  by 
selling  it  at  6  d.  per  gallon  above  cost  ? 

2,  Find  the  compound  interest  on  $66.67  for  2  years  at  9 

per  cent. 

3,  How  much  money  must  be  invested  in  3  per  cent  bonds 

at  92  to  secure  an  annual  income  of  $150? 

4,  Find  the  L.C.M.  of  12,  84,  120,  132,  156. 

5,  Keduce  -|-|-|-f  to  lowest  terms. 

6,  A  piece,  of  work  can  be  done  in  50  days  by  35  men. 

After  12  days  16  men  strike.     How  soon  will  the 
rest  finish  the  work  ? 


ARITHMETIC.  31 


61. 

1,  Find  the  greatest  common  measure  of  5522  and  6006. 

2,  Divide  TV-TV  by  3TV-2ff 

3,  Express  as  common  fractions  0.06125  and  0.1237. 

4,  If  a  room  is  27  feet  5  inches  long,  14  feet  7  inches  wide, 

12  feet  10  inches  high,  how  much  paper  -J-  of  a  yard 
wide  is  required  to  cover  the  walls  ? 

5,  "What  is  the  amount  at  simple  interest  of  $1275  in  5 

years  8  months  at  3|-  per  cent  ? 

6,  If  I  buy  sugar  at  $7  per  cwt.,  at  what  rate  per  pound 

must  I  retail  it  to  gain  7-f  per  cent  ? 


62. 

1.  If  8  men  can  reap  40  acres  of  wheat  in  7  days,  how 

many  acres  will  24  men  reap  in  28  days  ? 

2.  Find  the  square  root  of  2,900,209. 

3.  How  many  cubic  feet  of  air  in  a  room  10  feet  long,  8 

feet  6  inches  broad,  and  6  feet  6  inches  high  ? 

4.  A  4f  per  cent  stock  can  be  purchased  at  91.     What 

per  cent  interest  will  this  investment  yield? 

5.  When  the  Centigrade  thermometer  marks  25  degrees, 

what  will  Fahrenheit's  thermometer  mark  ? 

6.  Find  the  greatest  common  measure  of  210  ;  258  ;  903. 


32  EXAMINATION   MANUAL. 


63. 

1.  amplify  -I,    and    g^. 

* 

2.  Express  as  decimals  -^  yf TT»  anc^   ' — ^— •• 

db  1 

3.  How  many  miles  will  a  ploughman  walk,  in  ploughing  an 

acre  of  ground,  if  each  furrow  is  a  foot  in  breadth  ? 

4.  A  room  is  12£  feet  by  10  feet,  and  7  feet  high.     How 

many  yards  of  paper  2  feet  6  inches  wide  will  it 
take  to  paper  the  room,  if  the  waste  is  ten  per  cent  ? 

5.  A  plank  is  3  inches  thick,  18  inches  wide,  and  30  feet 

long.     How  many  board  feet  does  it  contain  ? 

6.  Eggs   are  sold  at  the  rate  of  5  for  4  cents.     At  what 

price  were  they   bought  if   the  profit  was  20  per 
cent? 

64. 

1.  Find   the   square   root   of    0.00027   to   four  places   of 

decimals. 

2.  If  I  sell  $2500  3  per  cent  stock  at  95,  and  invest  the 

proceeds  in  4?  per  cent  stock  at  par,  what  difference 
does  it  make  in  my  income  ? 

3.  What  is  the  cost  of  papering  a  room  16  feet  long,  12 

feet  wide,  10J  feet  high,  with  paper  21  inches  wide 
at  7  cents  per  yard,  if  the  waste  is  12J  per  cent? 

4.  Express  -%fa  as  a  decimal;  and  0.1236  as  a  common 

fraction. 

5.  Divide  22.4615  by  0.167  ;  and  0.004095  by  0.273. 

6.  Find  the  least  common  multiple  of  3,  8,  15,  21,  18. 


AEITHMETIC.  33 


65. 

1.  A  owns  £  of  a  vessel,  B  J,  and  C  ^,  and  the  rest  belongs 

to  the  master.     What  is  the  master's  share  ? 

2.  If  two  acres  will  maintain    3  horses  for  4  days,  how 

long  will  6  acres  maintain  6  hordes  ? 

3.  Divide  9.3828  by  1117;  by  11.17;  by  0.01117. 

4.  What  is  the  difference  between  the  simple    and  com- 

pound interest  on  $550  for  3  years  at  5  per  cent? 

5.  A  merchant  sold  goods  for  $750  more  than  he  paid  for 

them,  and  cleared  15  per  cent.  What  did  he  pay 
for  them  ? 

6.  Two  boats  row  a  race  of  1  mile  720  yards.     One  rows 

31  strokes  a  minute,  and  clears  30  feet  each  stroke ; 
the  other  rows  33  strokes,  and  clears  28  feet.  How 
many  yards  ahead  will  the  winning  boat  be  when  it 
passes  the  winning  post  ? 

66. 

1.  What  is  the  price  of  a  Turkey  carpet  20  feet  6  inches 

long  by  12  feet  9  inches  wide,  at  $5.04  a  square 
yard? 

2.  If  I  invest  $3570  in   7  per  cent  stock  at  2  premium, 

what  income  do  I  derive  from  it  ? 

3.  A  grocer  bought  40  pounds  of  tea  at  60  cents,  and  90 

pounds  of  coffee  at  42  cents  a  pound.  He  sold  the 
tea  at  96  cents  and  the  coffee  at  36  cents  a  pound. 
What  did  he  gain  or  lose  ? 

4.  Find  the  least  common  multiple  of  34,  51,  85,  120,  170. 

5.  Simplify  12.4  +  0.064-0.066, 

0.002 

6.  Add  i  of  |  of  5s.  4rf.,  |  of  f  of  6s.,  f  of  f  of  2s. 


34  EXAMINATION    MANUAL. 


67. 

1.  Find  the  cost  of  papering  a  room  21  feet  long,  16£  feet 

wide,  10J  feet  high,  at  15  cents  per  square  yard. 

2.  A  can  run  10  yards  to  B's  9.     How  many  yards  start 

must  A  give  B  in  a  mile  to  make  an  even  race  ? 

3.  Simplify  i—  H-H-I).  . 


i 


4.  If  I  sell  out  $10,000  of  3|  per  cent  stock  at  94£,  and 

buy  with  the  proceeds  6  per  cent  stock  at  105,  what 
will  be  the  alteration  in  my  income  ? 

5.  Find  the  true  discount  on  $1025.62^  for  6  months  at  5i 

per  cent  per  annum. 

6.  Reduce  to  its  lowest  terms  IH4M. 


68. 

1.    Find  the  L.C.M.  of  2,  3,  4,  5,  8,  12,  72,  84. 

+     °f 


a  ofA 

3.  Find  the  cost  of  paving  a  passage  15  yards  2  feet  6 

inches  long,  and  3  yards  6  inches  wide,  with  tiles 
costing  $3.60  per  square  yard. 

4.  Add  together  53£,  36.875,  4|,  I  of  7J,  and  divide  the 

result  by  0.01. 

5.  If  6  men  can  dig  5  acres  in  8  days  of  10  hours,  in  how 

many  days  of  12  hours  can  4  men  dig  6  acres  ? 

6.  At  what  rate  of  interest  will  $2560  amount  to  $3328 

in  5  years  ? 


ARITHMETIC.  35 


69. 

1.  If  I  sell  out  $1000  from  3  per  cent  stock  at  88,  and 

buy  5  per  cent  stock  at  110,  what  alteration  do  I 
make  in  my  income  ? 

2.  If  a  man  buys  560  tons  of  coal  at  14s.  8>d.  per  ton,  and 

sells  it  at  lie?,  per  cwt.,  what  is  his  gain  per  cent? 

3.  Divide  42.5  by  0.017  ;  and  find  the  value  of  0.625  of 

3  pounds  Avoirdupois. 


4.  Simplify  3  -ft  +  !)- 

5.  Find  the  square  root  of  1.00060009. 

6.  The  gross  yearly  rental  of  an  estate  is  $2100  ;  taxes  and 

repairs  amount  to  25  per  cent  of  the  rental.  The 
owner  sells  the  estate  for  21  times  the  gross  yearly 
rental,  and  invests  the  proceeds  in  3£  per  cent 
stock  at  98.  What  does  he  gain  or  lose  in  his  net 
income  ? 

70. 

1.  If  $1350  at  simple  interest  amount  to  $1570.50  in  1 

year  8  months,  find  the  rate  per  cent. 

2.  If  by  selling  wine  at  $3  a  gallon  I  lose  6  per  cent,  at 

what  price  must  I  sell  it  to  gain  17  £  per  cent? 

3.  Find  the  compound  interest  on  $750  for  5  years  at  2J 

per  cent. 

4.  Eeduce  347,894,178  square  inches  to  acres,  etc. 

5.  If  $850  amounts  to  $913.75  at  2£  per  cent,  find  the 

time. 

6.  A  room   is  10  feet  high,  5£  yards  long,   and  3  yards 

wide.  It  contains  a  door  8  feet  by  4  feet,  two 
windows  each  5  feet  by  4  feet,  and  a  fireplace  6  feet 
by  4  feet  6  inches.  How  many  square  yards  on  its 
walls  require  to  be  painted  ? 


36  EXAMINATION    MANUAL. 


71. 

1.  The  distance  between  the  posts  of  a  railway  telegraph 

is  60  yards.  Find  the  rate  of  a  train  which  passes 
11  posts  in  50  seconds. 

2.  Find  the  income  from  an   investment  of  $5308.33  in 

3  per  cent  bonds  at  91. 

3.  A  invests  $1200,  B  $2400,  in  business.     The  net  profit 

at  the  end  of  the  year  is  $  720.  How  much  should 
A  and  B  each  receive,  and  what  is  the  rate  of 
interest  upon  the  investment? 

4.  Find  the  least  common  multiple  of  5,  7,  16,  28,  48,  21. 

5.  If  i  of  a  ship  be  worth  $292.25,  what  part  of  her  will 

be  worth  $1002? 

6.  If  10  men  can  reap  20  acres  in  4  days,  how  many  men 

can  reap  70  acres  in  10  days? 

72. 

1.  What  sum  of  money  will  amount  to  $276.25  in  1  year 

and  3  months  at  5  per  cent  simple  interest  ? 

2.  When  3  per  cent  bonds  are  at  75,  what  sum  must  be 

invested  to  produce  an  annual  income  of  $  120  ?  • 

3.  Find  the  present  worth  of  $1836,  due  4  years  hence,  at 

5  per  cent  simple  interest. 

4.  What  is  the  rent  of  a  field  containing  112  acres  109.5 

square  rods  at  $2.64  an  acre? 

5.  Divide  1368.2394  by  2400.21,  and  by  0.00240021. 


ARITHMETIC.  37 


73. 

1.  Find  the  value  of  £2-f-i-  of  £140  10s.  6rf.  +  f  of  £1 

Is. 

2.  Find  the  greatest  common  measure  of  1288,  1736,  104. 

3.  If  120  men  build  a  house  60  feet  high  in  15  days,  how 

many  will  build  a  house  55  feet  high  in  10  days? 

4.  Find  the  difference  between  the  simple  and  compound 

interest  on  $955  at  6  per  cent  for  4  years. 

5.  A  garrison  of  1000  men  have  provisions  for  30  days. 

At  the  end  of  10  days  a  reinforcement  arrives,  and 
then  the  provisions  last  only  5  days.  What  is  the 
number  of  the  reinforcement? 


74. 

1.  Express  0.466  as  a  common  fraction. 

2.  A  sum  of  money  was  borrowed  at  5  per  cent  simple  in- 

terest. In  7  years  it  amounted  to  $810.  What  was 
the  sum  borrowed? 

3.  If  100  men  in  6  days  of  10  hours  can  dig  a  trench  200 

yards  long,  .3  yards  wide,  and  2  yards  deep,  in  how 
many  days  of  8  hours  can  180  men  dig  a  trench  360 
yards  long,  4  yards  wide,  and  3  yards  deep? 

4.  Find  the  cube  root  of  42,508,549. 

5.  How  many  rods  of  fencing  are  required  to  enclose  a 

square  park  containing  832  acres  105  square  rods? 

6.  Which  is  the  better  investment,  4  per  cent  stock  at  120, 

or  2$  per  cent  stock  at  75? 


38  EXAMINATION    MANUAL. 

75. 

1.  What  is  the  length  of  the  edge  of  a  cubical  cistern 

which  contains  as  much  as  a  rectangular  one  whose 
edges  are  154  feet  11  inches,  70  feet  7  inches,  and 
53  feet  1  inch  ? 

2.  For  what  must  I  sell  a  horse  that  cost  me  $75.50  so  as 

to  gain  5J  per  cent? 

3.  By  selling  12  pounds  of- tea  for  $7.56, 1  gain  5  per  cent. 

What  do  I  gain  or  lose  per  cent  by  selling  50  pounds 
of  the  same  tea  for  $31? 

4.  Find  the  amount  of  $4250  for  2  years  6  months  at  5 

per  cent  compound  interest. 

5.  Reduce  f ff  and  -|~f|-f  to  their  lowest  terms. 

6.  How  can  you  tell  without  dividing  whether  a  number 

is  exactly  divisible  by  11  ? 

76. 

1.  Find  the  amount  of  $7234.25  at  4J  per   cent  simple 

interest,  in  22  years  2  months  20  days. 

2.  If  20  men  build  a  wall  800  feet  long,  10  feet  high,  and 

18  inches  thick  in  14  days  of  8  hours,  how  thick  a 
wall  will  15  men  build  900  feet  long  and  15  feet 
high  in  21  days  of  9  hours  ? 

3.  Subtract  0.992748  from  1. 

4.  Find  the  cost  of  3  acres  145  square  rods  of  land,  at  $  120 

an  acre. 

5.  What  is  the  price  of  a  silver  bowl  weighing  5  pounds 

9  ounces  8  dwts.,  at  $1.40  per  ounce? 

6.  Add  together  &,  f ,  -&,  &&. 


ARITHMETIC.  39 


77. 

1.  How  many  tiles,  each  7  inches  square,  will  be  required 

to  cover  a  floor  19  feet  3  inches  by  13  feet  5  inches  ? 

2.  Extract  the  cube  root  of  0.145531576. 

3.  If  a  tradesman,  by  selling  an  article  at  $1.98,  loses  17£ 

per  cent,  what  should  he  have  sold  it  for  to  gain  40 
per  cent  ? 

4.  What  is  the  income  of  a  man  whose  income  tax  at  4  d. 

in- the  pound  amounts  to  23  guineas? 

5.  If  2  horses  can  plough  7  acres  of  ground  in  a  day,  how 

many  horses  will  plough  161  acres  in  \\\  days? 

6.  In  1,250,784  seconds,  how  many  weeks,  days,  etc.  ? 

78. 

1.  Divide  2054.95  by  0.0563. 

2.  A  merchant  sells  tea  to  a  tradesman  at  a  profit  of  60 

per  cent;  but  the  tradesman,  failing,  pays  only  12£ 
cents  on  the  dollar.  How  much  per  cent  does  the 
merchant  lose  by  the  sale  ? 

3.  When  a  3J  per  cent  stock  is  at  93,  find  what  price  a 

4J  stock  must  bear  that  an  investment  may  be  made 
with  equal  advantage  in  either  stock. 

4.  Find  the  cube  root  of  134,217,728. 

5.  Find  the  product  of  10£,  &,  ff  and  l£. 

6.  If  14  men  can  mow  168  acres  in  12  days  of  81  hours, 

how  many  acres  can  be  mowed  by  20  men  in  11 
days  of  7|  hours? 


40  EXAMINATION    MANUAL. 


79. 

1.  Between  the  years  1841  and  1851,  the  population  of 

England  increased  14-^-  per  cent.  In  1851,  the 
population  was  21,121,290.  What  was  it  in  1841  ? 

2.  A  merchant  has  teas  worth  $1.08   and   84  cents   per 

pound  respectively,  which  he  mixes  in  the  ratio  of 
3  pounds  of  the  first  kind  to  2  of  the  second  kind, 
and  sells  the  mixture  at  $1.04  per  pound.  What 
does  he  gain  or  lose  per  cent  ? 

3.  A  person  invests  $5460  in  3  per  cent  stock  at  91 ;  he 

sells  out  $2000  stock  when  it  has  risen  to  93?,  and 
the  remainder  when  it  has  fallen  to  85 ;  he  invests 
the  proceeds  in  4|  per  cent  stock  at  102.  What  is 
the  alteration  in  his  income  ? 

4.  Extract  the  cube  root  of  5.78  to  three  places  of  decimals. 

SO. 

1.  If  48  pioneers  in  5  days  of  12  J  hours  can  dig  a  trench 

139|  yards  long,  4J  yards  wide,  and  2J  yards  deep, 
how  many  hours  a  day  must  270  pioneers  work  for. 
42  days,  in  order  to  dig  a  trench  4910T1g-  yards  long, 
4-J  yards  wide,  and  3i  yards  deep  ? 

2.  If  a  man  rows  10  miles  in  2J  hours  against  a  stream, 

the  rate  of  which  is  3  miles  an  hour,  how  long  will 
he  be  rowing  5  miles  with  the  stream  ? 

3.  Find  the  price  of  5  acres  127  square  rods  and  88  square 

yards  at  $161£  per  acre. 

4.  If  a  person  selling  sugar  at  9J  cents  per  pound  loses 

1.0  per  cent,  what  did  he  give  per  hundredweight  ? 


ARITHMETIC.  41 


81. 

1,   A  square  contains  40,092.0529  square  feet.     Find  the 
length  of  one  of  its  sides. 


2    Simplify  (°-°75  X  °-°75)  ~  (Q-°05  X 
J~  0.75  —  0.05 

3,  A  person  invested  $4706  in  3  per  cent  stock  at  90  \  . 

A  year  afterwards,  when  the  3  per  cent  stock  had 
fallen  to  89,  he  sold  out  one-half  of  his  stock  and  re- 
invested it  in  5  per  cent  foreign  bonds  at  .52.  What 
change  did  the  reinvestment  make  in  his  income  ? 

4,  If  50  men  dig  a  trench  120  yards  long,  5  feet  broad,  10 

feet  deep  in  3  days  of  10  hours,  in  how  many  hours 
will  they  dig  a  trench  175  Yards  long,  4  feet  broad, 
and  8  feet  deep  ? 

5    Simplify  Si+iiiH     Si 
1117  X 


82. 

1,   Find  the  least  common  multiple  of  14,  36,  84,  108,  144. 

2    Einmlifr    9*-8»  +  6*-5* 
y8^-7|f  +  6i-5f 

3,  If  with  a  capital  of  $  500  a  tradesman  gains  $  50  in  7 

months,  in  what  time  will  he  gain  $  60.50  with  a 
capital  of  $385? 

4,  A    certain  4i    per  cent  stock  is  at  a  discount  of  23. 

What  income  should  I  get  from  $  385  invested  in  it  ? 

5,  Find  the  cost  of  papering  the  walls  of  a  room  10  feet  8 

inches  wide,  19  feet  4  inches  long,  and  9£  feet  high, 
with  paper  2  feet  wide  at  5  cents  a  yard,  allowing 
10  yards  of  the  paper  for  waste. 


42  EXAMINATION   MANUAL. 


83. 

1.  If  1  inch  of  rain  on  4840  square  yards  gives  18,200 

gallons  of  water,  how  many  gallons  will  0.875  of  an 
inch  on  a  square  mile  give  ? 

2.  If  the  amount  of  property  liable  to  income  tax  be  525 

million  pounds  sterling,  how  many  pence  in  the 
pound  must  the  tax  be  to  produce  17£  million 
pounds  ? 

3.  The  circumferences  of  two  of  the  wheels  of  an  engine  are 

25£  feet  and  16£  feet  respectively.  How  many 
more  times  will  one  turn  round  than  the  other  in 
4J  miles? 

4.  If  the  shadow  of  an  upright  pole  9  feet  high  be  7  J  feet, 

what  will  be  the  height  of  a  church  spire  which  casts 
a  shadow  247?  feet  long? 


,     Q.      ,., 
5.    amplify 


84. 


1.  Find  the  value  of  3.75  of  half-a-crown  (2|s.)  +  4.4  of  a 

guinea  (21s.)  +  1.024  of  £22. 

2.  Find  the  length  in  yards  of  the  side  of  a  square  enclosure 

which  contains  4  acres  144  square  yards. 

3.  A  plot  of  ground  50  yards  long  and  40  yards  wide  is  to 

be  covered  with  sods  1£  feet  long  and  6  inches 
broad.  If  the  sods  cost  75  cents  per  hundred,  what 
will  be  the  -expense  for  turf  alone  ? 

4.  Find  the  present  worth  of  $122.80  due  7  months  hence, 

at  4  per  cent. 

5.  In  a  town  where  the  annual  death  rate  is  2£  per  cent, 

the  average  number  of  deaths  a  week  (52  weeks  to 
the  year)  is  228.  What  is  the  population  of  the 
town? 


ARITHMETIC.  43 


85. 

1.  A  person  transfers  $3000  from  a  4  per  cent  stock  at  90 

to  a  3  per  cent  stock  at  72.  How  much  3  per  cent 
stock  can  he  purchase,  and  what  will  be  the  differ- 
ence in  his  income  ? 

2.  A  cistern  5  feet  deep,  16  feet  long,  4  feet  6  inches  wide, 

is  filled  by  one  pipe  in  45  minutes.  In  what  time 
will  a  cistern  6  feet  deep,  20  feet  long,  5  feet  wide, 
be  filled  by  3  similar  pipes  ? 

3.  Multiply  0.416  by  0.025,  divide  the  product  by  3.25, 

and  reduce  the  result  to  a  common  fraction. 

4.  A  -clothier  gains  25  per  cent  by  selling  cloth  at  $  5  per 

yard  ;  but  a  bale  of  80  yards  being  damaged,  he  has 
to  reduce  the  price  10  per  cent.  What  is  now  his 
profit  on  the  bale,  and  his  gain  per  cent  ? 

5.  Add  12^,  13fV>  17i  and  T&- 


86. 

i. 


2.  Find  the  difference  between  ^-  of  200  rods  and  -f$  of  £ 

of  a  mile. 

3.  What  fraction  of  560  pounds  is  equal  to  0.1590  of  a 

long  ton  ? 

4.  $13,000  of  31  per  cent  stock  is  sold  at  98.     How  much 

money  must  be  added  to  the  sum  realized  in  order 
to  secure  an  equal  income  in  3  per  cent  stock  at  87  ? 

5.  An  army  of  120,000  men  lost  15  per  cent  by  desertion 

to   the    enemy.     What   increase   per  cent  did   the 
enemy  gain,  their  number  previously  being  64,000? 


44  EXAMINATION    MANUAL. 


87. 

1.  In  1870  three  towns  had  populations  of  17,650,  19,600, 
and  18,760  respectively.  In  1880,  the  population 
of  the  first  had  decreased  18  per  cent,  that  of  the 
second  had  increased  21  per  cent,  while  the  popula- 
tion of  the  three  towns  had  increased  by  4691. 
Find  the  change  per  cent  in  the  population  of  the 
third  town. 


2.    What  fraction  of  V5|  is  V0.000225? 
5^  -  0.042  -  2.4  +  ?| 
'         16ft-*- 601 

4.  Find  the  square  root  of  1,079,521  and  0.1079521. 

5.  "What  is  the  gain  by  investing  $1950  at  971  and  selling 

out  at  104,  the  brokerage  on  each  transaction  being 
i  per  cent  ? 

88. 

o 

1.  Find  the  value  of  -  -  correct  to   four  places  of 

-  -,     •      -,          Vl9  -  4 
of  decimals. 

2.  Find  the  simple  interest  on  $281.60  at  3£  per  cent  for 

4  years  and  2  months. 

3.  By  selling  a  carriage  for  $73.15,  I  should  lose  5  per 

cent.  At  what  price  must  I  sell  it  to  gain  15  per 
cent? 

4.  Which   is   the   better  investment,  3  per  cent  stock  at 

64i,  or  5  per  cent  stock  at  1021  ? 

5.  A  person  has  a  certain  capital,  half  of  which  is  invested 

in  3  per  cent  stock  at  90,  and  the  other  half  in  5 
per  cent  at  110.  His  total  income  is  $6883.50. 
What  is  his  capital? 


ARITHMETIC.  45 


89. 

1.  At  what   rate   per    cent  will   a  given    sum  of  money 

double  itself  at  simple  interest  in  30  years  ? 

2.  A  grocer  has  tea,  which  he  must  sell  at  84  cents  per 

pound  to  gain  40  per  cent.  If  he  mixes  it  with  tea 
which  cost  him  54  cents  per  pound,  in  the  ratio  of  7 
of  the  best  kind  to  3  of  the  poorest,  and  sells  the 
mixture  in  10-pound  packages  at  $7.76,  how  much 
does  he  gain  per  cent? 

3.  How  many  times  is  224  pounds  2  ounces  contained  in 

6  long  tons  8  cwt.  8  pounds  ? 

4.  Find  -|-  of  8  miles  145  rods  3  yards  1  foot  6  inches. 

5.  The  sides   of  two    squares    contain  77  yards  1  foot  9 

inches,  and  7  yards  2  feet  4  inches,  respectively. 
Find  the  side  of  a  square  whose  area  is  equal  to 
the  sum  of  the  areas  of  the  two  squares. 

90. 

1.  If  a  railway  journey  of  177  miles   120  rods  takes  3 

hours  56?  minutes,  what  is  the  rate  per  hour? 

2.  Multiply  209   acres   145   square   rods  3  square  yards 

by  13. 

3.  Two  wines  worth  $8  and  $6  per  gallon  respectively  are 

mixed  together.  If  the  mixture  is  worth  $6.87? 
a  gallon,  in  what  ratio  are  they  mixed? 

4.  A  tradesman  pretends  to  charge  10  per  cent  above  the 

wholesale  price,  but  he  has  adulterated  his  goods 
with  50  per  cent  of  a  poorer  kind,  which  costs  only 
-§•  of  the  price.  What  is  his  real  rate  of  profit  ? 

5.  Express  as  decimals  -£%,  -^g-,  and  -/%. 


46  EXAMINATION   MANUAL. 

91. 

1.  If  the  2-penny  loaf  weighs  15  ounces  when  wheat  is  at 

8  shillings,  how  is  wheat  selling  when  the  Ss-penny 
loaf  weighs  2  pounds? 

2.  Find  exactly  the  cube  root  of  1,277,289^-. 

3.  Reduce  -^-ffflr  to  its  lowest  terms. 

4.  What  fraction  is  1  week  7  hours  12  minutes  of  the  time 

from  Jan.  1,  1800,  to  Feb.  20,  1864,  both  days  in- 
clusive ? 

5.  Find  the  circulating  decimal  equivalent  to  1  ^  1 . 

6.  At  what  rate  per  cent  will   a  person  receive  interest 

who  invests  his  capital  in  3  per  cent  stock  at  91  ? 

92. 

1.  At  what  price  must  a  person  buy  8  per  cent  stock  to 

receive  interest  at  the  rate  of  3£  per  cent? 

2.  If  a  vessel  sails  500  miles  in  2  days  18  £  hours,  how  far 

will  she  sail  between  May  20  at  noon,  and  8  o'clock 
on  the  morning  of  July  10  ? 

3.  A  person  buys  coffee  at  $24  per  cwt.,  and  chicory  at 

$10  per  cwt.,  and  mixes  them  in  the  ratio  of  2  of 
chicory  to  5  of  coffee.  He  retails  the  mixture  at  30 
cents  per  pound.  What  is  his  gain  per  cent  ? 

4.  A    and    B  enter  into  partnership.     A  puts  in  $2100, 

B  $1500.  Four  months  after,  C  enters  the  partner- 
ship with  $2700.  At  the  end  of  the  year  the 
profit  is  10  per  cent  on  the  whole  capital.  What 
share  of  the  profit  belongs  to  each  ? 

5.  If  oranges  are  bought  at  the  rate  of  20  for  25  cents, 

how  many  should  be  sold  for  $12  to  gain  40  per 
cent  on  the  cost  ? 


ARITHMETIC.  47 


93. 

1.  Find  the  ratio  of  the  rates  for  freight  on  two  railroads, 

one  of  which  charges  $5.62J  for  carrying  4200 
pounds  44  miles,  and  the  other,  $7.86£  for  carry- 
ing 5376  pounds  52|  miles. 

2.  If  the  discount  on  $127.925  for  20  days  be  $0.175,  find 

the  rate  per  cent. 

3.  A  gold  wreath,  weighing  3  pounds  7  ounces  12  dwt., 

cost  $1275.  If  it  is  made  of  gold  worth  $19.37| 
per  ounce,  what  is  charged  for  the  manufacture  ? 

4.  Divide  24.109932  by  301.28. 

5.  Find  the  value  of  0.90625  of  a  cubic  yard. 

6.  Simplify  3  \  +  3T%  +  2^  +  2 


94, 

1.  Reduce  18  days  5  hours  40  minutes  20  seconds  to  the 

fraction  of  31  days  21  hours  30  minutes  10  seconds. 

2.  Show  that  the  greatest  common  measure  of  two  num- 

bers is  the  least  common  multiple  of  all  their  com- 
mon measures. 

3.  A  bought  63  sheep,  and  sold  $  of  them  at  a  profit  of 

15  per  cent,  \  at  a  profit  of  50  per  cent,  and  the 
rest  at  a  loss  of  25  per  cent.  What  did  he  pay  for 
the  sheep,  if  his  gain  was  $19.25  on  the  whole? 

4.  Find  the  simple  interest  on  $500  for  8  years  3  months 

at  1J  per  cent. 

.5.    Find  the  cost  of  369  miles  120  rods  22  yards  of  tele- 
graph wire  at  $73.33^  per  mile. 


48  EXAMINATION    MANUAL. 


95. 

1.  What  sum  will  amount  to  $5431.80  in  6  years  at  4J 

per  cent  simple  interest? 

2.  Reduce  11  rods  4  yards  4.5  inches  to  the  decimal  of  a 

mile. 

3.  Find  the  greatest  common  measure  of  14,938,  23,474, 

32,010. 

4.  Find  the  number  of  seconds  from  the  beginning  of  the 

year  1883  to  Dec.  17,  9  A.M.,  and  express  the  result 
in  words. 

5.  Extract  the  cube  root  of  5  to  four  places  of  decimals. 

96. 

1.  Supposing  the  area  of  a  circle  to  be  3^-  times  the  square 

of  the  radius,  find  the  weight  of  a  circular  disc  of 
cast  iron  7  feet  in  diameter,  and  1-J  inches  thick, 
knowing  that  a  plate  1  foot  square  and  1  inch  thick 
weighs  37-^  pounds. 

2.  If  £  of  a  sheep  is  worth  $-f,  and  f  of  a  sheep  is  worth 

y1^  of  an  ox,  what  is  the  value  of  100  oxen  ? 

3.  Find  the  entire  surface  of  a  cube,  the  volume  of  which 

is  14  cubic  feet  705.088  cubic  inches. 

4.  Find  the   cost   of  a  draft  for  $400,  payable  60  days 

after  sight,  exchange  being  J  per  cent  discount,  and 
interest  7  per  cent. 

5.  A  man  bought  a  horse  for  $125  and  sold  him  for  $100. 

What  per  cent  of  the  cost  of  the  horse  did  he  lose  ? 

6.  Multiply  4  acres  67  square   rods  19   square   yards   4 

square  feet  72  square  inches  by.  27. 


ARITHMETIC.  49 


97. 

1.  In  what  time  will  the  simple  interest  on  $375,  at  4  per 

cent,  amount  to  $91.25? 

2.  Divide  the  number  702  into  3  parts,  proportional  to  £, 

i,  and  \. 

3.  Divide  75  miles,  79  rods,  3  yards  by  75. 

4.  How  many  bricks,  each   9   inches  by  4J  inches  by  3 

•  inches  are  there  in  a  pile  36  feet  long,  9  feet  wide, 
and  12  feet  high  ? 

5.  Find  the  face  of  a  draft,  payable  60  days  after  sight, 

that  can  be  bought  for  $1250,  when  exchange  is  at 
i  per  cent  premium,  and  interest  7  per  cent. 

6.  Find  the  square  root  of  0.9  to  four  places  of  decimals. 

98. 

1.  After  paying  ^  of  my  money  to  one  person,  -J  to  an- 

other, and  -fa  to  a  third,  I  had  7  cents  remaining. 
How  much  had  I  at  first  ? 

2.  A  person  walks  at  the  rate  of  3^-  miles  an  hour.    Three 

hours  after  he  has  set  out  on  a  journey,  he  is  fol- 
lowed by  another  person,  walking  at  the  rate  of  5 
miles  an  hour.  In  what  time  will  he  be  overtaken  ? 

3.  A  grocer  mixes  72  pounds  of  tea  at  69  cents  a  pound 

with  90  pounds  of  tea  at  60  cents  a  pound.  At 
what  price  per  pound  must  he  sell  the  mixture  so  as 
to  gain  10  cents  a  pound  ? 

4.  Extract  the  cube  root  of  J-  to  four  places  of  decimals. 

5.  At  what  rate  per  cent  will   $3000  produce  $250  in- 

terest in  1  year  2  months  and  24  days  ? 


50  EXAMINATION    MANUAL. 

99. 

1.  Find  the  interest  of  $1721.84  from  April  1  to  Nov.  12 

at  4|-  per  cent. 

2.  At  what  rate  per  cent  will  $1025.20  produce  $25.72 

interest  in  4  months  9  days  ? 

3.  Find  the  principal  that  will  produce  $1339.28  in  2  years 

7  months  24  days  at  6  per  cent  compound  interest. 

4.  Find   the   time    in    which    $793.875  will    amount   to 

$805.84  at  5£  per  cent. 

5.  Find  the  proceeds  of  the  following  note  : 

DETROIT,  Feb.  2,  1881. 

Four  months  after  date  I  promise  to  pay  to  the 
order  of  John  Horn  four  thousand  five  hun- 
dred fifty  and  f-fa  dollars,  value  received. 

JAMES  THORN. 

Discounted  at  a  bank  at  5|  per  cent,  Feb.  16. 

100. 

1.  A  bankrupt  has  goods  worth  $975,  and,  had  they  real- 

ized their  full  value,  his  creditors  would  have  re- 
ceived 81-J-  per  cent  of  their  claims ;  but  •§  of  the 
goods  were  sold  at  17-J-  per  cent,  and  the  remainder 
at  23J  per  cent  below  their  value.  How  many 
cents  on  the  dollar  did  the  bankrupt  pay  ? 

2.  Find  the  value  of  157  miles  144  rods  of  telegraph  wire 

at  $57.50  per  mile. 

3.  Reduce  fffi ,  -J^ff  to  tneir  lowest  terms,  and  express 

their  difference  as  a  decimal. 

4.  Extract  the  cube  root  of  1250.6894. 

5.  Extract  to  six  places  of  decimals  the  square  root  of  19. 


ARITHMETIC.  51 


101. 

1.  If  a  person  steps  80cm  at  each  step,  how  many  steps  will 

he  take  in  walking  round  a  square  field  containing 

18ha    625qm? 

2.  How  many  cords  of  wood  can  be  piled  in  a  woodshed 

128  feet  long,  42  feet  wide,  12  feet  high,  allowing 
for  a  driveway  10  feet  wide,  running  from  one  end 
of  the  building  to  the  other  ? 

3.  The  true  discount  on  a  bill  of  $470.89,  due  4  years 

hence,  is  $85.62 ;  find  the  rate  per  cent. 

4.  If  the  retail  price  of  a  book  is  $6,  and  25  are  sold  for 

$  102,  what  rate  per  cent  of  discount  is  allowed  ? 

5.  A  merchant  insures  a  cargo  whose  value  is  $4500  at  5 

per  cent.  For  what  sum  should  he  insure  so  as  to 
cover  both  the  loss  of  the  cargo  and  the  premium  ? 

6.  A  man  sent  $500  to  his  agent  in  Chicago,  with  which 

to  buy  flour.  The  agent  bought  flour  at  $5  a  bar- 
rel, charging  2J-  per  cent  commission  for  buying. 
How  many  barrels  of  flour  can  he  buy,  reserving 
for  himself  his  commission,  and  how  much  money 
will  be  left  over  ? 

102. 

1.  Find  the  sum  of    1871ccra,  5411,  4.51hl,  and  give  the 

answer  in  liters. 

2.  What  is  the  commission  on  goods  worth  $767.73  at  7|- 

per  cent  ? 

3.  Kequired  the  equated  time  for  the  payment  of  $700 

due  in  6  months,  $800  due  in  9  months,  and  $600 
due  in  10  months. 

4.  When  3  per  cent  stock  is  at  91  f,  find  how  much  can  be 

bought  for  $540,  allowing  i  per  cent  commission 
upon  the  stock  bought. 

5.  Find  the  cube  root  of  0.75  to  four  places  of  decimals. 

6.  If  2  men  can  reap  2-J  acres  in  2f  days,  how  long  will 

it  take  11  men  to  reap  15  acres? 


52  EXAMINATION   MANUAL. 


103. 

1.  If  it  takes  25  minutes  for  a  man  who  reads  2  pages  in 

3  minutes  to  read  a  certain  document,  how  long  will 
it  take  a  man  who  reads  a  page  a  minute  to  read  a 
document  3  times  as  long? 

2.  A  man  sells  $7500  of  6  per  cent  railway  stock  at  120, 

and  invests  half  the  proceeds  in  3  per  cent  stock  at 
93,  and  the  other  half  in  5-|-  per  cent  stock  at  90. 
Find  the  alteration  in  his  income. 

3.  A  piece  of  land  2449m  square  is  sold  for  $35  a  hektar. 

How  much  does  the  land  bring  ? 

4.  If  cloth  is  sold  for  $3.75  a  yard  at  a  loss  of  10  per  cent, 

what  should  be  the  selling  price  a  yard  to  gain  18 
per  cent  ? 

5.  Find  the  cube  root  of  0.3  to  four  places  of  decimals. 

104. 

1.  A  company  whose  capital  is  $2,500,000  pays  an  annual 

dividend  of  6|-  per  cent,  besides  paying  a  tax  of  1-J 
per  cent  on  its  whole  capital.  Find  the  total  annual 
receipts,  the  expenses  being  60  per  cent  of  the  gross 
receipts. 

2.  Bought  4  lots  of  wool  at  $652.50  each,  and  sold  the 

whole  at  20  per  cent  profit.  What  was  the  selling 
price  per  lot  ? 

3.  If  the  increase  in  the  number  of  male  and  female  crim- 

inals is  1|-  per  cent,  while  the  decrease  in  the  num- 
ber of  males  alone  is  4f  per  cent,  and  the  increase 
in  the  number  "of  females  is  9£  per  cent,  find  the 
ratio  of  male  criminals  to  female  criminals. 

4.  Find  the  cost  of  a  carpet  75cm  wide,  at  $4.25  a  meter, 

for  a  room  5.25m  long,  and  4.75m  wide,  strips  run- 
ning across  the  room,  if  there  is  a  total  waste  of  3m 
in  matching  the  pattern. 

5.  Extract  the  square  root  of  0.2  to  five  decimal  places. 


ARITHMETIC.  53 


105. 

1.  An  army  lost  18  per  cent  of  its  strength  by  sickness 

and  desertion,  and  then  lost  14  per  cent  of  the  re- 
mainder in  battle.  The  number  left  was  84,624. 
Of  how  many  did  the  army  originally  consist  ? 

2.  If  6  iron  bars  4  feet  long,  3  inches  broad,  and  2  inches 

thick  weigh  288  pounds,  how  much  will  15  weigh, 
each  6£  feet  long,  4  inches  broad,  and  3  inches 
thick  ? 

3.  Find  the  cost  of  plastering  a  room  13m  long,  12m  wide, 

and  7m  high,  at  30  cents  a  square  meter,  if  115qm  are 
allowed  for  base-board,  doors,  etc. 

4.  Find  the  cube  root  of  25  to  three  places  of  decimals. 

5.  In  1841,  the  population  of  Great  Britain  was  21,476,000, 

and  that  of  Ireland  7,310,000.  In  1851,  the  popu- 
lation of  Great  Britain  had  increased  8.45  per  cent, 
and  that  of  Ireland  had  decreased  12.5  per  cent. 
Find  the  increase  per  cent  in  the  population  of  the 
whole  kingdom. 

106. 

1.  A  ship,  valued  at  $14,500,  is  insured  at  3?  per  cent, 

and  her  cargo,  valued  at  $32,000,  is  insured  at  5 
per  cent.  Find  the  whole  cost  of  insurance. 

2.  Into  how  many  pills  of  325mg  each  can  a  mass  of  23.4g 

be  made? 

3.  The  solid  contents  of  a  cube  is  37  cubic  feet,  £4  cubic 

inches.  Find  the  cost  of  painting  its  outside  at 
33i  cents  per  square  foot. 

4.  What  must  be  the  side  of  a  cubical  cistern,  which  will 

contain  exactly  1000  imperial  gallons  of  water,  if  an 
imperial  gallon  contains  277.274  cubic  inches? 

5.  If  a  compound  consist  of  1185  parts  copper,  715  parts 

tin,  and  100  parts  zinc,  find  the  percentage  of  each 
metal  in  the  compound. 


54  EXAMINATION    MANUAL. 


107. 

1,  A  rectangular  cistern  9  feet  long,  5  feet  4  inches  wide, 

2  feet  3  inches  deep  is  filled  with  a  liquid  that 
weighs  2520  pounds.  How  deep  must  a  cistern  be 
that  will  hold  3850  pounds  of  the  same  liquid,  if  its 
length  is  8  feet,  and  its  width  5  feet  6  inches  ? 

2,  Reduce  to  prime  factors,  and  then  find  the  greatest  com- 

mon measure  of  35,035,  41,580,  24,255. 

3,  How  many;  square  slabs  of  marble  150qcm  on  the  surface 

will  be  required  to  pave  a  court  whose  area  is 
50.70qm? 

4,  A  person  sells  out  his  3  per  cent  stock  at  86 1,  and  gets 

$34,000 ;  he  invests  one  half  of  this  sum  in  4  per  cent 
stock  at  97,  and  the  remainder  in  3£  per  cent  stock 
at  94.  Find  the  alteration  in  his  income. 

5,  If  56  cubic  feet  1044  cubic  inches  of  timber  are  required 

to  floor  a  room  29^  feet  by  25i  feet,  what  is  the  thick- 
ness of  the  boards  ? 

108. 

1,  A  merchant  has  teas  worth  $1.12?  and  87-J  cents  per 

pound  respectively,  which  he  mixes  in  the  ratio  of 
3  pounds  of  the  better  kind  to  2  of  the  poorer  kind, 
and  sells  the  mixture  at  $1.08i  per  pound.  What 
does  he  gain  or  lose  per  cent  ? 

2,  How  many  revolutions  will  the  wheels  of  a  carriage 

make  in  travelling  41km,  if  the  wheels  are  125cm  in 
diameter?  (The  circumference  is  3.1416  times  the 
diameter.) 

3,  In  what  proportion  must  wines  worth  $3,  $4,  $5.20, 

$6,  per  gallon  be  mixed,  so  as  to  give  a  profit  of 
14|-  per  cent  when  sold  for  $4.80  a  gallon? 

4,  Extract  to  four  figures  the  cube  root  of  20. 

5,  If  a  railway  train  goes  27f  miles  in  2f  hours,  how  far 

will  it  go  in  an  hour? 


ARITHMETIC.  55 


1O9. 

1,  In  what  time  will  §2275  amount  to  $2673.12£  at  5  per 

cent,  simple  interest? 

2,  If  a  horse  trots  23f  miles  in  2?  hours,  what  is  his  rate 

per  hour  ? 

3,  If  twelve  men  can  build  a  wall  6  feet  high,  3  feet  thick, 

in  9  days,  how  many  men  would  build  a  wall  of  the 
same  length,  5  feet' high,  4  feet  thick,  in  24  days? 

4,  A  man  pays  $12,000  for  5a  of  land,  and  sells  it  for 

$25.20  a  square  meter.     How  much  does  he  make? 

5,  A  river  30  feet  deep  and  200  yards  wide  flows  4  miles 

an  hour.  Find  the  number  of  cubic  feet  of  water 
that  passes  a  given  point  in  a  minute. 

6,  Extract  to  four  figures  the  cube  root  of  0.002. 

110. 

1,  A  cistern  has  two  pipes,  one  of  which  can  fill  it  in  2 

hours,  the  other  in  3  hours.  A  third  pipe  can 
empty  it  in  5  hours.  If  all  these  are  opened  when 
the  cistern  is  empty,  in  what  time  will  it  be  filled? 

2,  A  pile  of  wood  is  8.50m  long,  2.66m  wide,  2.60m  high. 

How  many  sters  of  wood  are  there? 

3,  A  clock  is  set  at  12   o'clock  on  Monday ;    at  noon  on 

Tuesday  it  is  3  minutes  too  fast,  What  will  be  the 
true  time  when  the  clock  strikes  4  on  Thursday 
afternoon  ? 

4,  If  20  men  can  do  a  piece  of  work  in  12  days,  how  many 

men  will  do  another  piece  of  work  six  times  as 
great  in  -^  of  the  time  ? 

5,  If  5  per  cent  be  lost  by  selling  an  article  at  $2.50,  find 

the  gain  or  loss  per  cent  by  selling  it  at  $  3.12|, 

6,  Find  the  square  root  of  53107.2025. 


56  EXAMINATION    MANUAL. 


Ill 

1.  Reduce  167,948,604  square  inches  to  acres,  etc. 

2.  A  man  contracts  to  perform  a  piece  of  work  in  30  days, 

upon  which  he  employs  15  men.  In  24  days  it  is 
only  half  finished.  How  many  additional  men  must 
he  employ  to  finish  the  work  in  time  ? 

3.  A  cistern  can  be  filled  by  a  spout  in  2  hours,  but  on 

account  of  a  leak  in  the  cistern  the  spout  takes  2-j- 
hours  to  fill  it.  How  long  will  it  take  the  leak  to 
empty  the  cistern  ? 

4.  A  country,  the  population  of  which  is  |LO  millions,  has 

births  yearly  of  1  in  20,  and  deaths  1  in  30.  What 
will  its  population  be  5  years  hence  ? 

5.  A  beam   is   14.14m  long.     Its    other    dimensions    are 

51.6cm,  174mm.     Find  its  volume. 

6.  If  a  trader  sells  13|-  pounds  for  14  pounds,  how  much 

per  cent  does  he  gain  fraudulently  ? 

112. 

1.  A  wine  which  contains  7J  per  cent  of  spirit  is  frozen, 

and  the  ice,  which  contains  no  spirit,  is  removed. 
The  proportion  of  spirit  in  the  wine  thus  is  increased 
to  8J  per  cent.  How  much  water  in  the  shape  of 
ice  is  removed  from  504  gallons  of  the  original  wine  ? 

2.  Find    to   four  places  of  decimals    the  square  root   of 

0.001  and  of  0.5 ;  and  also  find  what  numbers  have 
0.1  and  0.03  for  their  square  roots. 

3.  The  diameter  of  a  carriage  wheel  is  4  ft.     Two  persons 

calculate  the  number  of  its  turns  in  a  given  distance, 
one  calling  the  circumference  3  times  the  diameter, 
the  other  3-f  times ;  their  results  differ  by  100  turns. 
Find  the  distance. 

4.  A  package  of  candles  which  weighs  465g  is  sold  for  28 

cents.     What  is  the  price  of  10kg  of  the  candles  ? 

5.  Reduce  to  its  lowest  terms  the    roduct  of  1 


ARITHMETIC.  57 


113. 

1.  Resolve  into  prime  factors  5940,  19,008,  and  269,568, 

and  write  the  greatest  number  that  will  divide  them 
all  without  remainder,  and  the  smallest  number 
that  they  will  all  divide  without  remainder. 

2.  Divide  181.3  by  0.00037,  and  by  37,000. 

3.  Find  the  cost  of  carpeting  a  room  18  feet  6  inches  long, 

12  feet  6  inches  wide,  with  carpet  f  of  a  yard  wide, 
at  75  cents  per  yard,  strips  running  lengthwise,  and 
3  yards  being  allowed  for  matching  the  patterns. 

4.  If  3  men  mow  20  acres  in  11  days  of  11  hours,  how 

many  men  will  it  take  to  mow  a  rectangular  field 
384  yards  long  and  300  wide,  in  4  days  of  12  hours  ? 

5.  The  difference  between  the  simple  and  compound  inter- 

est on  a  sum  for  3  years  at  5  per  cent  is  $23.12J. 
Find  the  sum. 

6.  How  many  hektars  in  a  square  kilometer? 

114. 

1.  A  box  is  3.75m  long,  3.50m  wide,  and  50cm  high.     Find 

how  many  liters  of  olive  oil  it  will  hold,  and  the 
weight  of  the  oil  in  kilograms,  the  specific  gravity 
of  the  oil  being  0.914. 

2.  If  A  can  do  f  of  a  piece  of  work  in  4  hours,  and  B  can 

do  f  of  the  remainder  in  1  hour,  and  0  finish  it  in 
20  minutes,  in  what  time  will  they  do  it,  all  work- 
ing together  ? 

3.  When  a  common  fraction  is  reduced  to  a  decimal,  in 

what  cases  will  the  result  be  a  terminating  decimal, 
and  in  what  cases  a  circulating  decimal  ? 

4.  If  by  selling  goods  for  $272  I  lose  15  per  cent,  how 

much  per  cent  would  I  have  lost  or  gained  if  I  had 
sold  them  for  $336? 

5.  If  oranges  are  bought  at  the  rate  of  20  for  a  dollar,  how 

many  should  be  sold  for  $28  to  gain  40  per  cent? 

6.  Find  the  cube  root  of  84.9  to  three  places  of  decimals. 


58  EXAMINATION    MANUAL. 


115. 

1.  If  a  man  walk  11  yards  in  5  seconds,  how  long  will  lie 

be  in  walking  a  mile  ? 

2.  A  cubic  foot  of  water  weighs  62-1  pounds,  and  a  room 

18  feet  9  inches  by  13  feet  4  inches  is  flooded  to  a 
depth  of  2  inches.  What  is  the  weight  of  water  in 
the  room  ? 

3.  Assuming  that  3  hektars  contain  35,881  square  yards, 

and  that  one  hektar  contains  10,000  square  meters, 
find  the  length  of  a  meter  in  yards. 

4.  Add  together  536.421,  53,642.1,  5.36421,  and  subtract 

the  result  from  100,000. 

5.  If  the  price  of  candles  8J  inches  long  be  18  cents  for 

a  half-dozen,  and  that  of  candles  of  the  same  thick- 
ness and  quality  10*  inches  long  be  22  cents  a  half- 
dozen,  which  kind  would  you  advise  a  person  to  buy, 
and  what  would  be  the  saving  per  cent  if  your 
advice  is  followed  ? 

116. 

1.  Find   the   weight   in   kilograms    of   the    air  in  a  hall 

23m  long,  16m  wide,  and  10m  high,  the  specific  gravity 
of  air  being  0.00129206. 

2.  A  cubical  block  contains  9  cubic  feet,  1029  cubic  inches. 

Find  the  number  of  square  yards,  etc.,  in  its 
surface. 

3.  A  bar  of  metal  weighing  100  ounces  16  dwts.  is  made 

into  coins,  each  weighing  1  ounce  8  dwts.  How 
many  coins  are  there  ? 

4.  A  person  investing  in  a  3  per  cent  stock  received  3i 

per  cent  interest  on  his  money.  What  is  the  price 
of  the  stock? 

5.  A  bar  of  gold,  weighing  196  pounds  10  ounces  10  dwts., 

is  cased  in  lead,  weighing  24  pounds  14  ounces. 
Find  the  weight  of  the  whole  in  Avoirdupois  weight. 


ARITHMETIC.  59 


117. 

1.  A  merchant  buys  4000  bushels  of  wheat,  one-fifth  of 

which  he  sells  at  a  gain  of  5  per  cent,  one-fourth  at 
a  gain  of  10  per  cent,  one-half  at  a  gain  of  12  per 
cent,  and  the  remainder  at  a  gain  of  16  per  cent. 
If  he  had  sold  the  whole  at  a  gain  of  11  per  cent, 
he  would  have  made  $35  more.  "What  was  the 
cost  of  the  wheat  per  bushel  ? 

2.  If  1000  square  yards  of  land  produce  a  load  of  hay, 

how  many  loads  will  25  acres  produce  ? 

3.  Assuming  8000  meters  to  be  equal  to  5  miles,  find  the 

number  of  square  meters  there  are  in  an  acre. 

4.  A  person  having  a  certain  sum  of  money  to  invest  finds 

that  an  investment  in  5  per  cent  stock  at  11 7?  will 
yield  him  $29  more  interest  annually  than  an  in- 
vestment in  3  per  cent  stock  at  92J.  How  much 
money  has  he  to  invest  ? 

5.  Find  the  simple  interest  on  $281.63  at  3s  per  cent  for 

4  years  and  2  months. 

118. 

1.  A  freight  train  is  8  miles  ahead  of  an  express  that  travels 

at  the  rate  of  a  mile  in  H  minutes.  20  minutes 
later  the  express  runs  into  the  freight  train.  At 
what  rate  is  the  freight  train  running  ? 

2.  A  man  bought  240  cows  at  Rotterdam,  paying  $71.50 

for  each.  He  paid  -^  of  their  cost  for  their  trans- 
portation, and  exchanged  them  for  299  horses  which 
he  sold  for  $  75  apiece.  What  did  he  gain  per  cent 
on  his  expenditure  ? 

3.  If  a  square  field  contain  10.24ha,  find  the  length  of  its 

side  in  meters. 

4.  Find  the  amount  for  $512  for  3  years  at  6|  per  cent, 

compound  interest. 

5.  If  a  field  containing  5i  acres  produces  112  bushels  of 

wheat,  what  is  the  area  of  a  field  which  will  pro- 
duce 400  bushels  of  wheat  at  the  same  rate  ? 


60  EXAMINATION    MANUAL. 

119. 

1,  Multiply  4  acres  67  square    rods   19  square   yards  4 

square  feet  72  square  inches  by  27. 

2,  What  is  the  weight  of  a  cubic  centimeter  of  water  ?  of 

a  liter  of  water?  of  a  cubic  meter  of  water?  If  a 
cubic  meter  of  gravel  weighs  2.11  metric  tons,  what 
is  its  specific  gravity  ? 

3,  If  7  men,  working  16  days,  can  mow  a  field  1320  yards 

long,  and  880  yards  wide,  what  will  be  the  length 
of  the  side  of  a  field  1320  yards  wide,  which  4  men 
can  mow  in  42  days  ? 

4,  Divide  1.765  by  2470  to  five  places  of  decimals. 

5,  If  8  acres  produce  220  bushels  of  corn,  how  much  will 

22  square  yards  produce  ? 

120. 

1,  If  3  acres  of  land  cost  $465.90,  how  much  can  be  bought 

for  $6716.725? 

2,  From  0.315  of  a  gallon  take  2.25  pints. 

3,  $19.68f  is  2^  per  cent  of  what  sum? 

4,  A,  B,  and  C  rent  a  farm  for  $270.     A  puts  200  sheep 

on  it ;  B,  150 ;  and  C,  100.  After  6  months  A  sells 
f  of  his  flock  to  C,  and  3  months  later  B  sells  f  of 
his  to  A.  How  much  of  the  rent  should  each  pay 
at  the  end  of  the  year  ? 

5,  How  many  times  a  minute  does  the 'wheel  of  a  carriage 

turn,  when  the  carriage  is  driven  at  the  rate  of 
14km  an  hour,  and  the  diameter  of  the  wheel  is  120cm? 


ARITHMETIC.  61 


121. 

1,  If  a  man  walks  llm  in  5  seconds,  how  many  kilometers 

can  he  walk  in  an  hour  at  the  same  rate  ? 

2,  Find  the  cost   of  repairing  a  road  87  yards  1  foot  10 

inches  long,  at  the  rate  of  $4  a  rod. 

3,  A  cask  that  weighs  236  pounds  4  ounces  just  sinks  in  a 

square  cistern  of  water,  whose  edge  is  2  feet  6 
inches.  If  the  cask  is  removed,  how  far  will  the 
water  sink  in  the  cistern,  reckoning  the  weight  of  a 
cubic  foot  of  water  to  be  1000  ounces  ? 

4,  A  man  paid  $45.10,  including  a  duty  of  10  per  cent,  for 

a  watch.     How  much  was  the  duty  ? 

5,  If  19  men  can  build  38  yards  of  wall  in  12  days,  how 

many  will  build  96  yards  2  feet  3  inches  in  214- 

'      i? 


122. 

1,  Find   the  amount  of  $875  at  the  end  of  1  year  and 

3  months,  at  4  per  cent  per  annum,  compound  inter- 
est, the 'interest  accruing  quarterly. 

2,  If  12  men  build  a  wall  60  feet  long,  4  feet  thick,  and 

20  feet  high  in  24  days,  working  12  hours  a  day, 
how  many  men  will  it  take  to  build  a  wall  100  feet 
long,  3  feet  thick,  and  12  feet  high,  in  18  days, 
working  8  hours  a  day  ? 

3,  If  the  specific  gravity  of  sea-water  is  1.026,  and  that  of 

olive  oil  is  0.915,  what  is  the  weight  of  a  hektoliter 
of  each  in  kilograms  ? 

4,  What  must  be  the  length  of  an  inner  edge  of  a  cubical 

box  which  will  hold  10  cubic  feet  ? 

5,  An  agent,  charging  2i  per  cent  commission,  receives  for 

his  services  $313.     Find  the  amount  of  his  sales. 


62  EXAMINATION    MANUAL. 


123. 

1.  An  agent  received  $5922  with  which  to  purchase  goods, 

and  is  allowed  5  per  cent  commission  on  his  pur- 
chase. If  the  $5922  covers  the  cost  of  the  goods 
and  his  commission,  how  much  was  his  commission? 

2.  How  much  per  cent  above  cost  must  a  man  mark  his 

goods  in  order  that  he  may  take  off  30  per  cent 
from  the  market  price,  and  still  make  30  per  cent 
on  the  cost? 

3.  If  a  pint  contains  2&J  cubic  inches,  how  many  pints  are 

there  in  a  cubic  foot  of  water  ? 

4.  If  14  liters  of  water  be  poured  into  a  vessel  containing 

'  6  liters  of  sulphuric  acid,  specific  gravity  1.84,  and 
the  mixture  shrink  to  19.944  liters,  what  is  the  spe- 
cific gravity  of  the  mixture  ? 

5.  Find  0.015  of  17  acres  130  square  rods. 

124. 

1.  If  5  needlewomen  can  finish  a  certain  quantity  of  work 

in  10J-  days  of  9f  hours  each,  how  long  would  it  take 
3  needlewomen  to  do  twice  the  same  work,  reckon- 
ing 10  hours  to  the  day  ? 

2.  Find  the  square  root  of  0.196  to  four  places  of  decimals. 

3.  Find  the  greatest  common  measure  of  837,  1134,  and 

1347. 

4.  A  ship  carries  5  chronometers,  and  estimates  Greenwich 

time  by  the  mean  time  of  the  five.  Two  of  them 
lose  respectively  39  seconds  in  35  days,  and  4.3 
seconds  in  6  days  ;  the  others  gain  respectively  5 
seconds  a  week,  1.3  seconds  a  day,  and  23  seconds  in 
14  days.  By  how  much  will  the  estimated  time  be 
in  error  after  a  cruise  of  176  days? 

5.  How  many  square  meters  of  surface  will  240   sheets 

cover,  if  the  sheets  are  303mm  long  and  195mm  wide  ? 


ARITHMETIC.  G3 


125. 

1,  A  bankrupt  owes  $5050.    His  assets  are  $378.75.    How 

many  cents  does  he  pay  on  a  dollar  ? 

2,  If  36  men  dig  a  trench  72  yards  long,  4  yards  wide,  and 

3  yards  deep,  how  many  men  will  be  required  to 
dig  one  80  yards  long,  4  yards  wide,  and  6  yards 
deep  in  the  same  time  ? 

3,  Eeduce  to  its  simplest  form  the  expression 

3  of  it  of  ?£-  1-1- 

0±          0t          *  i 


4,  A  person  invests  $6534  in  3  per  cent  stock  at  90,  and 

on  the  stock  rising  to  91  transfers  his  stock  to  3-J-  per 
cent  stock  at  93-J-.  How  is  his  annual  income 
affected? 

5,  Olive  oil  costs  60  cents  a  kilogram.     What  is  the  price 

of  a  hektoliter,  if  the  specific  gravity  of  the  oil  is 
0.914? 

126. 

1,  The  distance  between  two  places  measured  on  a  military 

map  is  156mm.  What  is  the  actual  distance  between 
the  places  if  the  map  is  made  on  the  scale  of  1  to 
80,000  ? 

2,  How  many  horses  will  be  required  to  plough  117  acres  in 

35  days,  if  10  horses  can  plough  13  acres  in  7  days? 

3,  If  I  buy  3090  yards  of  cloth  at  92|  cents  per  yard,  and 

sell  the  whole  for  $3205.87|,  what  is  the  gain  per 
cent? 

4,  Find  the  amount  of  $7123.13  at  4  per  cent,  for  2  years 

and  3  months,  compound  interest. 

5,  How  many  bricks  81  inches   long,  4i  inches  wide,  2s 

inches  thick  can  be  stored  in  a  building  17  2  yards 
long,  10  yards  wide,  and  8J-  feet  high? 


G4  EXAMINATION    MANUAL. 


127. 

1.  How  many  panes  of  glass  40cm  by  80cm  will  be  required 

for  the  windows  of  a  house  if  the  total  surface  of 
measurement  of  the  glass  in  the  windows  is  203.52qm? 

2.  A  20  horse-power  engine  pumps  40  gallons  of  water 

from  a  pit  100  yards  deep  in  3  hours.  What  quan- 
tity of  water  will  an  engine  of  35  horse-power 
pump  from  a  depth  of  235  feet  in  141  days,  work- 
ing night  and  day  ? 

3.  A    speculator  buys  280  yards  of  carpet,  expecting  to 

sell  the  whole  at  $1.38  a  yard,  and  thereby  make 
15  per  cent  profit ;  but  40  yards  being  ruined,  what 
did  he  gain  or  lose  per  cent  by  selling  the  remainder 
at  the  expected  rate  ? 

4.  If  a  piece  of  land  is  bought  for  §3500,  and  a  man  who 

owns  -|  of  it  sells  %  of  his  share  for  $800,  how  much 
does  he  gain  per  cent  by  the  transaction  ? 

5.  Extract  the  cube  root  of  1.105507304. 

128. 

1.  A  tank  is  1.50m  wide,  3.20m  long,  and  80cm  deep.     How 

many  kilograms  of  alcohol,  specific  gravity  0.80, 
will  be  required  to  fill  it  one-third  full  ? 

2.  How  many  men  working  for  11  cents  an  hour  for  23 

days  of  9  hours  can  earn  the  same  wages  as  22  men 
working  for  11-J-  cents  an  hour  for  18  days  of  9^  hours. 

3.  If  goods  cost  $75.87-J-,  at  what  price  must  they  be  sold 

to  gain  17^-  per  cent? 

4.  A  can  mow  f  of  a  field  in   7|  days,  B  can  mow  f  of 

the  same  field  in  9J  days.  In  what  time  can  A  and 
B  together  mow  the  field  ? 

5.  A  train  travels  a  certain  distance  in  4-f%  hours  at  the 

rate  of  16|-  miles  an  hour.  How  long  will  a  train 
going  19 J  miles  an  hour  take  to  travel  the  same 
distance  ? 


ARITHMETIC.  65 


129. 

1.  A  rectangular  sheet  of  tin  of  uniform  thickness  is  85cm 

wide,  2.7m  long,  and  weighs  536g.  What  is  its 
thickness,  reckoning  the  specific  gravity  of  tin  at 
7.3? 

2.  I  pay  for  180  yards  of  cloth  at  92-J  cents  per  yard,  but 

it  is  measured  with  a  yard-stick  -f  of  an  inch  short. 
How  much  money  does  the  seller  unfairly  take  ? 

3.  What  must  a  person  have  invested  in  3  per  cent  stock 

at  93^-,  if  a  transfer  of  -f  of  his  capital  to  5  per 
cent  stock  at  125  would  increase  his  income  $14.80? 

4.  If  20  shillings  weigh  3  ounces  12  dwts.  12  grains,  and 

contain  5  dwts.  lOij-  grains  alloy,  how  much  pure 
silver  is  there  in  a  half-crown  (2J  shillings)? 

5.  Express  by  a  common  fraction  the  difference  between 

2.535  and  2.535. 

130. 

1.  A,  B,  and  C  rent  a  field  for  $25.62.     A  puts  in  15 

sheep  for  6  months,  B  45  sheep  for  8  months,  C  81 
sheep  for  4  months.  What  should  each  pay  toward 
the  rent? 

2.  The  top  of  a  building  236  feet  high  is  reached  by  a 

flight  of  steps,  each  12cm.  high.  Find  the  number 
of  steps,  if  a  meter  is  taken  as  equal  to  3  feet  Si- 
inches. 

3.  How  many  ars  of  land  in  a  strip  lkm  long  and  7m  wide? 

4.  An  executor  of  an  estate  finds  it  encumbered  with  debts 

to  the  amount  of  $4322.50  over  and  above  its  real- 
ized value  of  $10,729.50.  How  many  cents  on  a 
dollar  can  he  pay  the  creditors? 

5.  Extract  the  cube  root  of  437.245479. 


66  EXAMINATION    MANUAL. 


131. 

1.  What  fraction  of  a  pound  avoirdupois  is  a  pound  Troy, 
and  what  fraction  of  an  ounce  Troy  is  an  ounce 
Avoirdupois? 

2  * 


3,  Find  the  weight  in  kilograms  of  a  bar  of  gold  10cm  long, 

30mm  wide,  and  25mm  thick,  its  specific  gravity  being 
19.36. 

4,  If  $15  be  gained  on  $360  in  8  months  15  days,  what 

sum  will  gain  $21  in  1  year  6  months? 

5,  For  how  much  must  a  man  give  his  note  to  a  bank,  on 

4  months  at  6  per  cent,  to  obtain  $500? 

132. 

1,  What  sum  will  amount  to  $1104.75  in  3  years  at  3£  per 

cent,  compound  interest  ? 

2,  What  annual  income  will  be  produced  by  $13,000  in  a 

3  J  per  cent  stock  at  91  ? 

3,  If  the  circumference  of  a  coach-wheel  measures  17  feet 

7.2  inches,  how  often  will  it  turn  round  in  travelling 
8  miles  264  feet? 

4,  Keduce  to  its  lowest  terms  -g-f|-J. 

5,  If  a  square  meter  =  1550.031  square  inches,  find  to  the 

fifth  decimal  place  the  number  of  square  centimeters 
in  a  square  inch,  and  the  number  of  acres  in  a  hektar. 


ARITHMETIC.  67 


133. 

1,  A  tradesman's  prices  are  20  per  cent  above  cost  price. 

If  he  takes  10  per  cent  off  from  the  bill  of  a  custo- 
mer, what  per  cent  profit  does  he  make  ? 

2,  If  a  man  can  do  a  piece  of  work  in  77  hours,  and  a  boy 

can  do  the  same  work  in  121  hours,  in.  how  many 
hours,  minutes,  and  seconds  can  they  do  it,  working 
together  ? 

3,  If  the  cost  of  papering  a  room  8J-  yards  long,  6f  yards 

wide,  with  paper  2  feet  wide  at  8  cents  a  yard  be 
$14.32,  find  the  height  of  the  room. 

4,  If  3  per  cent  more  be  gained  by  selling  a  horse  for 

$83.25  than  by  selling  him  for  $81,  what  is  the 
cost  of  the  horse  ? 

5,  If  a  cubic  yard  =  0.76453cbm,  find  to  the  fifth  decimal 

place  the  number  of  cubic  centimeters  in  a  cubic 
inch,  and  the  number  of  sters  in  a  cord. 

134. 

1,  By  selling  out  $4500  of  5  per  cent  stock  at  112J,  and 
investing  the  proceeds  in  a  7  per  cent  stock,  a  per- 
son increases  his  income  by  $168. 75.  What  is  the 
price  of  the  7  per  cent  stock  ? 

2,  simplify  2fj  x  mn- 

3,  If  a  gram  =  15.43235  grains,  find  to  the  fifth  decimal 

place  the  number  of  pounds  Avoirdupois  in  a  kilo- 
gram and  in  a  metric  ton. 

4,  An  article  which  costs  $  95.76  per  cwt.  of  112  pounds  is 

retailed  at  $1.08  a  pound.  If  there  is  a  waste  of 
5  per  cent,  what  is  the  rate  per  cent  of  profit? 

5,  Find  the  square  root  of  0.1  to  four  places  of  decimals. 


68  EXAMINATION    MANUAL. 

135. 

1,  Find  the  L.C.M.'of  7,  11,  21,  63,  91,  99,  117. 

2,  A  plate  of  iron  137cm  long,  643mm  wide,  43.1mm  thick 

weighs  277.54kg.     What  is  its  specific  gravity?  - 

3,  If  135  men   can  dig  a  trench  48  yards  long,  1  foot  3 

inches  wide,  3  feet  9  inches  deep,  in  5  days  of  6 
hours,  how  many  men  will  be  required  to  dig  a 
trench  90  yards  long,  2  feet  6  inches  wide,  3  feet 
deep,  in  27  days  of  10  hours  ? 

4,  A  man  has  £  10  13  s.  4  d.  a  week  in  rents.     His  tenants 

cheat  him  out  of  y1-^  of  his  rent ;  he  pays  4  d.  in  the 
pound  for  collection,  and  9&  d.  in  the  pound  for 
taxes.  How  much  a  week  has  he  to  spend  ? 

5,  Divide  4900  by  0.07,  multiply  the  quotient  by  0.63,  and 

divide  the  result  by  0.049. 

136. 

1,  If  -f%  of  a  cargo  be  worth  $  750,  how  much  is  -£$  of  -f$  of 

it  worth? 

2,  A  parcel  of  5  pounds  7  ounces  is  carried  120  miles  for 

40  cents.  How  much  will  it  cost  to  carry  16  pounds 
5  ounces  a  distance  of  90  miles  at  the  same  rate-? 

3,  If  a  meter  =  39.37043  inches,  find  to  the  fifth  decimal 

place  the  number  of  centimeters  in  an  inch,  and  the 
number  of  kilometers  in  a  mile. 

4,  Find  the  cube  root  of  7.6  to  four  places  of  decimals. 

5,  A  person,  by  selling  an  article  which  cost  60  cents  a 

pound  at  67 -J  cents  a  pound,  makes  5  per  cent  more 
profit  than  if  he  had  sold  the  whole  for  $267.67£. 
Find  the  amount  sold. 


ARITHMETIC.  69 


137. 

1,  Find  the  sum  of  %  7T\,  8^,  19,  10|i  12f . 

2,  A  garrison  of  1000  men,  provisioned  for  60  days,  was 

reinforced  at  the  end  of  18  days,  and  the  provisions 
were  exhausted  at  the  end  of  30  days  from  that 
time.  Of  how  many  men  did  the  reinforcement 
consist? 

3,  Two  engines  40  miles  apart  ars  approaching  each  other 

at  the  rates  of  25  and  35  miles  an  hour.  Determine 
the  time  and  place  of  their  meeting. 

4,  Find  the  simple  interest  on'$  2187.50  for  219  days  at  4* 

per  cent,  reckoning  365  days  to  the  year. 

5,  Find  the  area  of  a  field  225m  long,  100m  wide.     Express 

the  answer  in  hektars  and  ars. 

138. 

1,  From  2000  subtract  852.2534,  and  divide  the  remainder 

by  16.38. 

2,  If  I  invest  $1200  in  3  per  cent  stock  at  72,  what  is  my 

income,  and  what  rate  per  cent  do  I  get  on  my 
investment? 

3,  If  $36  worth  of  bread  will  be  sufficient  for  12  men  8 

months,  when  corn  is  $  1  per  bushel,  how  many  men 
will  require  $100  worth  of  bread  for  12  months, 
when  corn  is  $  1.311  per  bushel? 

4,  Find  the  time  required  to  travel  3Pm  150m,  at  1  minute 

28  seconds  a  kilometer. 

5,  A  broker  receives  $6150  to  invest  in  cotton  at  10i  cents 

a  pound.  His  commission  is  21  per  cent  for  buy- 
ing. How  many  pounds  of  cotton  can  he  buy  ? 


70  EXAMINATION    MANUAL. 


139. 

1.  A  collector's  commission  for  collecting  taxes,  at  H  per 

cent,  is  $41.31.     What  is  the  sum  collected? 

2.  How  many  yards  of  carpeting  2  feet  8  inches  wide  will 

be   required  for  a  floor  19  feet  7  inches  long,  16 
.     feet  9   inches  wide,   if  the    strips   run   across   the 
room,  and  2|  yards  are  allowed  for  waste  in  match- 
ing the  pattern. 

3.  Find   the  value    of  a   carboy  (171)  of  sulphuric  acid, 

specific  gravity  1.841,  at  5  cents  a  kilogram. 

4.  If  the  ratio  of  the  circumference  to  the  diameter  be 

3.1416,  find  the  diameter  of  a  cylinder  whose  cir- 
cumference is  16J  feet. 

5.  How  much  more  income  will  a  person  have  by  trans- 

ferring $3975  of  3  per  cent  stock  into  3|-  per  cent 
stock,  if  the  price  of  the  3  per  cent  stock  is  93f , 
and  of  the  3J  per  cent  stock  99f? 

140. 

1.  Find   the   bank  discount  upon  a  note  of  $587,  given 

Feb.  29,  1880,  for  3  months,  and  discounted  April 
30  at  6  J  per  cent. 

2.  Determine  the  number  of  cubic  meters  in  a  box  2  yards 

long,  1  yard  wide,  and  2}  feet  deep,  reckoning  a 
cubic  yard  =  0.76453cbm. 

3.  A  reservoir  is  24  feet  8  inches  long,  and  12  feet  9  inches 

wide.  How  many  cubic  feet  of  water  must  be 
drawn  off  to  make  the  surface  sink  one  foot  ? 

4.  Divide  200  acres  into  four  parts  proportional  to  the 

numbers  50,  35,  80,  and  9. 

5.  Extract  the  cube  root  of  946,966,168. 


ARITHMETIC.  71 


141. 

1.  If  coffee  worth  66  cents,  77   cents,  and  57  cents  per 

pound  be  mixed  in  equal  quantities,  and  the  mix- 
ture sold  at  702  cents  per  pound,  what  is  the  gain 
or  loss  per  cent  ? 

2.  If  3  men,  working  11  hours  a  day,  can  reap  20  acres 

in  11  days,  how  many  men,  working  12  hours  a 
day,  will  reap  a  field  360  yards  long  and  320  yards 
broad,  in  4  days? 

3.  Find  in  yards  the  side  of  a  square  field  containing  15 

acres  109  square  rods  3  square  yards. 

4.  A  man  walks  10J  miles   the  first  day,  16£,  18 J,  27|, 

21J-  miles  on  the  four  following  days  respectively. 
He  then  returns  home  by  the  same  road  in  four  days. 
What  was  his  average  daily  walk  on  his  way  home 
and  on  his  whole  journey  ? 

5.  How  many  tons  of  air,  specific  gravity  0.00129206,  in  a 

space  70m  by  50m  by  35m  ? 

142. 

1.  By  selling  a  horse  for  $64.75, 1  lost  7J  per  cent.    What 

per  cent  should  I  have  gained  by  selling  him  for 
$73.50? 

2.  The  proceeds  of  the  income  tax  at  5c?.  in  the  pound 

was  equal  to  £5,250,000,  How  much  would  the 
proceeds  be,  if  the  tax  was  5  per  cent  ? 

3.  Find  the  number  of  liters  in  a  vat  2m  by  75cm  by  50cm. 

Also  find  the  weight  in  kilograms  of  sulphuric  acid, 
specific  gravity  1.840,  required  to  fill  it. 

4.  One   horse    goes    1}    miles   in    2    minutes  26  seconds ; 

another,  If  miles  in  3  minutes  36  seconds.  How 
much  per  cent  does  the  first  one  go  faster  than  the 
second  ? 

5.  Find  the  greatest  common  measure  of  j-f ,  2J,  4,  and  5}. 


72  EXAMINATION    MANUAL. 

143. 

1,  Find  the  least  common  multiple  of  y1^-,  2-J-,  5,  6J,  and  -fa. 

2,  By  selling  goods  for  $116.85  I  lose  5  per  cent.     For 

what  should  I  sell  them  to  gain  3|  per  cent? 

3,  A  spends  £  of  his  money,  then  i  of  the  remainder,  and 

then  J  of  what  he  has  left.  He  finally  has  $25. 
How  much  had  he  at  first  ? 

4,  Make  out  a  bill  and  receipt  it,  and  show  how  much 

change  there  will  be  from  a  twenty-dollar  bill : 
3J  cwt.  of  coal,  at  21  cents  a  cwt. ;  13  pounds  of 
cheese,  at  15J  cents  per  pound;  2f  pounds  of 
tea,  at  80  cents  per  pound ;  17  pounds  of  sugar, 
at  11  cents  per  pound;  3?  yards  of  flannel  at 
47  cents  per  yard ;  29  yards  of  gingham  at  21 J 
cents  a  yard. 

5,  Find  the  number  of  sters  in  a  pile  of  wood  4.50m  long, 

2m  wide,  and  2.50m  high. 

144. 

1,  If  7  men  earn  $31  in  9^  days,  how  much  will  17  men 

earn  in  2Gf  days  ? 

2,  Two  persons  have  each  a  capital  of  $12,000.     The  one 

invests  in  3  per  cent  stock  at  90f ;  the  other  in  5 
per  cent  stock  at  1031 .  What  is  the  difference  in 
their  incomes  ? 

3,  If  I  buy  14  sheep  for  $157.29,  and  sell  6  of  them  for 

$7.20  each,  for  how  much  a  head  must  the  re- 
mainder be  sold,  that  I  may  gain  4  per  cent  on  the 
whole  ? 

4,  Find  the  G.C.M.  of  1908,  936,  630,  21,294,  306. 

5,  A  hektoliter  of  rape-seed  weighs  63kg,  and  321  of  oil  can 

be  extracted  from  it.  How  many  kilograms  of  the 
seed  will  it  take  to  make  a  hektoliter  of  the  oil  ? 


ARITHMETIC.  73 


145. 

1,  The  volume  of  a  cube  is  2  cubic  yards  14  cubic  feet  145 

cubic  inches.  Find  its  edge,  and  also  its  diagonal 
to  two  places  of  decimals. 

2,  By  using  false  weights  a  grocer  receives  17  cents  instead 

of  16  cents.  Find  the  number  of  ounces  in  his  false 
pound,  and  his  gain  per  cent. 

3,  A  railway  pays  3i  per  cent  dividend.     At  what  price 

will  its  shares  give  4?  per  cent  to  a  purchaser? 

4,  A  person  sells  his  3  per  cent  stock  for  73£,  and  buys 

with  the  proceeds  3-i  per  cent  stock  at  81  T,  thereby 
increasing  his  income  $4.50.  How  much  3  per  cent 
stock  has  he  ? 

5,  Reduce  150  hektars  to  acres,  supposing  a  square  meter 

equal  to  1.196  square  yards. 


146. 

1,  A  profit  of  $127.60  is  made  by  selling  2552  pounds  of 

butter  at  45  cents  a  pound.  Find  the  cost  per 
pound  and  the  gain  per  cent. 

2,  For  what  sum  must  I  insure  goods  worth  $2192  at  2£ 

per  cent,  so  as  to  cover  their  value  and  the  premium 
paid? 

3,  If  $11.20  worth  of  paper  is  required  for  a  room  25  feet 

3  inches  long,  19  feet  9  inches  wide,  and  12  feet  high, 
when  the  paper  is  f  of  a  yard  wide,  find  the  cost  of 
each  yard  'of  paper. 

4,  Find    the    price    of  paving  .a    courtyard    25.34m   long, 

18.36m  wide,  at  $1.08  per  square  yard.  (Square 
meter  =  1.196  square  yards.) 

5,  Find  within  an  inch  the  diagonal  of  a  square  field  con- 

taining 3£  acres. 


74  EXAMINATION    MANUAL. 

147. 

1,  .Find  the  difference  between  30  chains,  15  links,  and 

126  rods.  Express  the  answer  in  yards  and  decimal 
of  a  yard. 

2,  Find  the  number  of  feet,  board  measure,  in  a  stick  of 

timber  15  inches  square  and  32  feet  long. 

3,  A  watch  is  10  minutes  too  fast  at  noon  on  Monday,  and 

loses  3  minutes  10  seconds  a  day.  Find  the  time 
indicated  by  the  watch  when  the  true  time  is  a 
quarter  past  ten  on  the  Sunday  morning  following. 

4,  Find   the  cost  of  5  acres  127   square  rods   88   square 

yards  at  $161.33^  per  acre. 

5,  Find  the  weight   in  metric    tons  of  a  block  of  stone 

12.37m  long,  7.14m  wide,  83cm  thick,  if  the  specific 
gravity  of  the  stone  is  2.5. 

148. 

1,  From  two  places  which  are  154  miles  apart  two  persons 

set  out  to  meet  each  other,  one  walking  at  the  rate 
of  3  miles  in  2  hours,  the  other  5  miles  in  4  hours. 
In  how  many  hours  will  they  meet  ? 

2,  A  regiment  was  reduced  to  520  men  after  engaging  in 

two  battles,  in  the  first  of  which  it  lost  1  man  in 
every  25,  and  in  the  second  -fg  of  the  remainder. 
How  many  men  were  there  at  first  ? 

3,  Find  the  cube  root  of  11  to  four  places  of  decimals. 

4,  Frenchmen,  on  the  average,  consume  yearly  1160g  of  coffee 

and  9g  of  tea;  and  Englishmen,  473g  of  coffee  and 
1679g  of  tea.  If  tea  be  3s.  and  coffee  Is.  8d.  per 
pound,  and  a  franc  be  worth  10^  d.,  find  in  francs  the 
value  of  an  Englishman's  consumption  above  a 
Frenchman's. 

5,  Find  the  value  of  2  pounds  5  ounces  8  dwts.  4  grains 

of  silver  at  $  125  an  ounce. 


ARITHMETIC.  75 


149. 

1.  Find  the  cost  of  30  3-inch  planks,  24  feet  long  and  11 

inches  wide,  at  §15  per  M. 

2.  An  agent  sells  2200  barrels  of  flour  at  $4.50  a  barrel, 

and  charges  2=}  per  cent  commission.  He  invests 
the  proceeds  in  steel  at  I?  cents  a  pound,  charging 
!-•>-  per  cent  commission.  What  is  his  entire  com- 
mission ? 

3.  Two  circular  gold  plates,  each  1  inch  thick  and  6  arid 

8  inches  in  diameter  respectively,  are  melted  into 
one  plate  of  the  same  thickness.  Find  the  diameter 
of  this  plate,  knowing  that  the  area  of  a  circle 
varies  as  the  square  of  its  diameter. 

4.  Find  the  cube  root  of  0.25  to  four  decimal  places. 

5.  How  many  miles  will  be  travelled  in  1  hour  28  min- 

utes 21  seconds  at  the  rate  of  50km  an  hour  ? 


150. 

1.  An  agent  sells  1000  barrels  of  flour  at  $5.50  a  barrel, 

and  charges  2 2  per  cent  commission  ;  expenses  for 
freight,  etc.,  are  $500.  With  the  net  proceeds  he 
buys  sugar  at  GT  cents  a  pound,  charging  2£  per 
cent  commission.  How  much  sugar  does  he  buy? 

2.  Find  the  number  of  feet  board  measure  in  25  joists, 

each  6  inches  by  4  inches,  and  14  feet  long. 

3.  Find  the  value  of  3  pounds  8  ounces  16  dwts.  12  grains 

of  gold  at  £3  17s.  lOic?.  per  ounce. 

4.  A   pond  whose  area  is  3  acres  is  frozen  over  with  ice 

to  the  uniform  thickness  of  6  inches.  If  a  cubic 
foot  of  ice  weighs  896  ounces,  find  the  weight  of 
ice  on  the  pond  in  long  tons. 

5.  A  jar  full  of  water  \veighs  1.325kg ;   filled  with  mercury, 

it  weighs  12.540kg.  What  is  the  capacity  of  the 
jar  and  its  weight?  The  specific  gravity  of  the 
mercury  is  13.59. 


EXAMINATION   PAPERS  IN  ARITHMETIC. 


BOWDOIN  COLLEGE,  BRUNSWICK,  ME. 
Examination  for  Admission,  June,  1883. 

1.  Find  the  difference  between  0.0000005  and  0.00005. 

2.  Change  0.03125  to  a  common  fraction  in  its  lowest  terms. 

3.  If    the    year    is    considered    365.25    days   instead    of 

365.242264,  how  great  will  the   error  be  in  1880 
years  ? 

4.  The  dividend  is  7423.973,  the  quotient  is  12.130,  and 

the  remainder  is  0.413.     What  is  the  divisor? 

5.  What  is  the  cost  of  60.5  tons  of  coal  when  0.9  of  a  ton 

cost  1 6.66? 

6.  Find  the  square  root  of  6.7081.     Of  0.004  to  the  nearest 

ten  thousandth.     Of  ^V 

7.  Keduce    6453m    to   kilometers.      4.15m    to    centimeters. 

6.451  to  milliliters.     How  many  decigrams  does  a 
dekaliter  of  pure  water  weigh  ? 

II. 

DARTMOUTH  COLLEGE,  HANOVER,  N.H. 

Entrance  Examination,  June,  1883. 

1.  Find  the  G.C.D.  of  66,  308,  and  506. 

2.  Divide  ||  by  Ltl 


78  EXAMINATION    PAPERS. 

3.  Give  the  value  of  the  kilometer  in  feet ;  of  the  kiloliter 

in  gallons  ;  of  the  kilogram  in  pounds. 

4.  If  there  is  a  gain  of  12-*-  per  cent  on  tea  at  90  cents  per 

pound,  what  would  be  the  gain  per  cent  at  84  cents 
per  pound? 

I  1  23 

5.  Find  -*! — —f —  to  four  decimal  places. 

il  U.Uu^jO 


III. 

BROWN  UNIVERSITY,  PROVIDENCE,  R.I. 

Examination  for  Admission,  June,  1883. 

1.  Reduce  -J-  of  6  per  cent  of  1.05  ~-  -fa  of  T7-g-  to  the  simplest 

form. 

2.  If  17  men  can  reap  a  field  in  9  days,  how  long  would  it 

take  to  reap  half  of  it  if  5  men  refuse  to  work  ? 

3.  A  man  bought  200m  of  cloth  in  France  at  16J  francs  a 

meter ;  he  paid  12J  cents  a  yard  for  duty  and 
freight,  and  sold  it  in  Boston  at  $4.62|-  a  yard. 
What  was  the  gain  ?  (1  franc  =  19.3  cents.) 

IV. 

MASS.  INSTITUTE  OF  TECHNOLOGY,  BOSTON,  MASS. 

Entrance  Examination,  June,  1882. 

1.  Find  the  L.C.M.  of  105,  476,  and  306. 

2.  A  grocer  makes  a  mixture  of  which  21.5  pounds  contains 

\  pound  of  rye,  12  pounds  of  wheat,  5  pounds  of  oats, 
and  4  pounds  of  barley.  How  much  of  each  ingre- 
dient will  be  contained  in  100  pounds  of  the  mix- 
ture? 


ARITHMETIC.  79 


3.  Reduce  to  a  decimal  fraction  — 3— .  and  from  it  subtract 

0.01  of  I.  a°*> 

4.  In  how  many  days  will  $3245  gain  $80  at  7  per  cent, 

simple  interest  ? 

5.  Find  the  G.C.D.  of  119  and  231. 

6.  Find  the  cube  root  of  0.012326391. 

7.  How  many  liters   are    contained  in  a  cubical  box  13 

inches  long,  13  inches  wide,  and  13  inches  deep  on 
the  inside  ?     (Given  that  lm  =  39.37".) 

8.  How  many  grams  of  distilled  water  will  such  a  box 

contain  ? 

V. 

Entrance  Examination,  Sept.,  1882. 

1.  Reduce   -S—^5  to  its  simplest  form. 

9T  +  5¥ 

2.  Reduce   —?  to  a  decimal  fraction. 

3.  A  and  B  together  have  $136,  and  -f  of  A's  money  is 

equal  to  -|  of  B's.     How  much  has  each? 

4.  At  $6.25  per  ton,  how  many  tons  of  coal  can  I  buy  for 

$1000,  and  allow  2-|-  per  cent  commission? 

5.  Find  the  square  root  of  0.00028562  to  ten-thousandths. 

6.  Floor  10m  by  6.5m,  carpet  90cm  wide  ;  .find  cost  of  carpet 

at  $1.25  per  meter. 

7.  In    a    parallelogram,    given   base  —  640dkm,    altitude  = 

180dkm  ;  find  area  in  hektars. 

8.  A  cylindrical  vessel  lm  high  is  made  of  sheet-iron  2cm 

thick,  and  holds  1001.     What  is  its  outer  diameter  ? 


80  EXAMINATION    PAPERS. 

VI. 

HARVARD  COLLEGE,  CAMBRIDGE,  MASS. 

Examination  for  Admission,  June,  1883. 

1.  Find  the  difference  between  3J  X  6ff  and  £i& 

2.  A  field  is  SS-/^  rods  long,  and  37?  rods  wide.     Find  its 

area  in  acres  and  square  rods.     (Acre  =  160  square 
rods.) 

3.  Find  all  the  factors  common  to  1001  and  616. 

4.  The  distance  from  Boston  to  Albany  is  320km.     Find  the 

distance  in  miles,  assuming  the  meter  to  equal  3-^- 
feet. 

5.  A  man,  travelling  9  hours  a  day,  goes  234  miles  in  15 

days.     How  far  can  he  go  in  30  days,  travelling  8 
hours  a  day  ? 

VII. 

YALE  COLLEGE,  NEW  HAVEN,  CT. 

Examination  for  Admission,  June,  1883. 

1.  Divide  82.1   by  41,  8.21    by  0.41,  and  0.821    by  410. 

Carry  the  result  in  each  case  to  four  decimal  places. 

2.  Find  the  value  to  three  decimal  places  of 


o    TV   -A  T2      1  i      133 

3.  Divide  *  X      by  —  - 


4.  Some  sugar  is  adulterated  as  follows  :  -fy  is  worth  8 
cents  per  pound,  %  is  worth  10  cents  per  pound,  y2-^ 
is  worth  12  cents  per  pound,  and  the  remainder,  33 
pounds,  is  sand.  What  is  the  mixture  worth  per 
pound  ? 


ARITHMETIC.  81 


5.  Bank  stock  which  sells  at  170  pays  an  annual  dividend 

of  12  2  per  cent.    What  rate  of  interest  does  a  buyer 
receive  ? 

6.  Find  the  depth  in  meters  of  a  cubical  cistern  which  has 

a  capacity  of  30,000*.     Give  the. result  to  three  deci- 
mal places. 

VIII. 

SHEFFIELD  SCIENTIFIC  SCHOOL,  NEW  HAVEN,  CT. 

Entrance  Examination,  June,  1883. 

1.  Find  the  G.C.D.  of  36,864  and  20,736. 

2.  Multiply  f  of  jjf  by  f  of  i. 

3.  (i.)  Give  the  table  of  metric  weights. 

(ii.)  A  cubical  cistern  holds  1331kg  of  water ;  what  is  the 
length  of  an  inner  edge  ? 

4.  Divide  67.56785  by  0.035,  and  multiply  the  result  by  £. 

Explain   the   position    of  the   decimal   point   after 
'division. 

5.  How  much   money   should   be   received    on  a  note  of 

$  1000,  payable  in  4  months,  discounting  at  a  bank 
where  the  interest  is  6  per  cent  ? 

6.  If  a  man  travel  117  miles  in  15  days,  employing  only 

9  hours  a  day,  how  far  would  he  go  in  20  days, 
travelling  12  hours  a  day  ? 

7.  Extract  the  square  root  of  10  to  five  places. 

IX. 

Entrance  Examination,  Sept.,  1883. 

1.  (i.)  Select  the  prime  numbers  between  50  and  100. 
(ii.)  What   is   the   least    number    that    can    be    exactly 
divided  by  ^  2£,  5,  %  and  ^? 


82  EXAMINATION   PAPERS. 

2.  Reduce  0.00096  to  its  simplest  equivalent  common  frac- 

tion. 

3.  7465  is  33£  per  cent  of  what  number  ? 

4.  A  broker  bought  84  shares  of  railroad  stock  at  19  per 

cent  discount.  He  sold  35  shares  at  27J  per  cent 
discount,  and  the  balance  at  8  per  cent  discount. 
Did  he  gain  or  lose,  and  how  much? 

5.  Calculate  the  cube  root  of  3.7-  to  five  decimal  places. 

6.  Give  the  approximate  value  of  the  meter  in  feet ;  of  the 

kilogram  in  pounds  Avoirdupois. 

7.  Find  the  weight  in  kilos  of  15  gallons  of  water. 

X. 

AMHERST  COLLEGE,  AMHERST,  MASS. 

Examination  for  Admission,  June,  1883. 

1.  From  10  take  six  millionths. 

2.  Divide  3.6412  by  400. 

3.  Reduce  0.0625  to  a  common  fraction  in  its  lowest  terms. 

4.  Find  the  G.C.D.  of  1235  and  1495. 

5.  How  many  rods  of  fence  will  be  required  to  enclose  640 

acres  of  land  in  a  square  form? 

6.  What  is  the  difference  in  time  between  Boston  and  San 

Francisco,  the  longitude  of  the  first  being  W.  71°  3' 
30",  and  the  second,  W.  122°  24' 40"? 

7.  Sold  a  pair  oxen  for  $175,  and  gained  5  per  cent ;  what 

per  cent  would  I  have  gained  if  I  had  sold  them  for 
$200? 

8.  If  6  men  in  15  days  earn  $135,  how  many  dollars  will  9 

men  earn  in  18  days  ? 

9.  What  is  the  weight  of  27hl  of  water? 


ARITHMETIC.  83 


XI. 

WILLIAMS  COLLEGE,  WILLIAMSTOWN,  MASS. 

Entrance  Examination,  June,  1883. 

1.  Reduce  -f-  to  a  decimal,  and  extract  the  square  root  to 

three  places. 

2.  How  long  must  the  side  of  a  square  lot  be  to  contain 

one  acre  of  ground  ? 

3.  Find  the  interest  on  $1385.50  for  23  days  at  7  per  cent. 
'4.   Reduce  532km  to  miles. 

XII. 

TUFTS  COLLEGE,  COLLEGE  HILL,  MASS. 

Examination  for  Admission,  June,  1881. 

1.  Find  the  L.C.M.  of  108,  217,  54,  31. 

2.  Find  the  prime  factors  of  927,  342,  861.     With  these 

prime  factors  get  the  Gr.C.D  of  the  given  numbers. 


3    Reduce  the  fraction 

JLofH     2'of.I 

12      f      4      11 

4.  If  the  rate  of  discount  is  5  per  cent  per  annum,  how 

much  can  be  obtained  on  a  note  for  $600,  payable 
in  4  months,  discounted  at  a  bank  ? 

5.  If  from  the  retail  price  of  a  book  20  per  cent  is  deducted, 

and  a  discount  of  10  per  cent  is  made  on  the  bal- 
ance, and  then  the  book  sells  for  $1.33,  what  is  the 
retail  price  ? 

6.  What  is  the  meter  ?     Name  its  subdivisions.     In  9780m 

how  many  kilometers  ?  Give  the  units  of  volume  in 
the  metric  system;  also,  of  weight. 

7.  What  weight  of  mercury  will   a  vessel   contain  whose 

capacity  is  20ccm,  the  mercury  being  13.5  times  as 
heavy  as  water? 


84  EXAMINATION    PAPERS. 

XIII. 

TEINITY  COLLEGE,  HARTFORD,  «CT. 

Examination  for  Admission,  June,  1883. 

1.  From  the  sum  of  of  and  4-J  subtract  6^-,  multiply  the 

difference  by  f  of  J-J  of  88,  and  find  what  fraction 
the  product  is  of  999. 

2.  Find  the  amount  of  $  342.42,  from  Feb.  5,  1ST.  ,  to  March 

15,  1881,  with  interest  at  7  per  cent;  and  reduce  it 
to  pounds  sterling  ? 

3.  What  is  the  weight  of  water  in  a  tank,  if  it  would  take 

98  minutes  to  empty  it,  at  the  rate  of  8.71  a  minute  ? 
If  it  were  filled  with  oil  at  $18.75  a  hektoliter, 
what  would  the  contents  be  worth  ? 

XIV. 

WESLEYAN  UNIVERSITY,  MIDDLETOWN,  CT. 

Examination  for  Admission,  June,  1883. 
\        3     ,5 


1.  Express   the  value  of   -  -  -  -  -  -   exactly  as  a 

decimal. 

2.  What  was  the  amount  due  January  15,  1883,  on  a  note 

for  §175,  dated  April  1,  1882,  bearing  5£  per  cent 
interest  ? 

3.  A  merchant  sold  \  of  a  certain  lot  of  goods  at  a  gain  of 

18  per  cent,  *  at  a  loss  of  5  per  cent,  and  the  re- 
mainder at  half  cost.  Did  he  lose  or  gain?  What 
per  cent  ? 

4.  Extract  the  square  root  of  0.01952,  carrying  the  result  to 

four  places  of  decimals. 


ARITHMETIC.  85 


5.  What  is  the  cost  of  digging  a  cellar  3dkm  wide,  5dkm  4m 

long,  and  2m  6dcm  deep,  at  the  rate  of  50  cents  a 
stere  ? 

6.  Two  men  undertake  to  do  a  piece  of  work  for  $6.00. 

One  could  do  it  alone  in  5  days,  the  other  in  8  days. 
With  the  assistance  of  a  boy,  they  finish  it  in  21 
days.  How  should  the  money  be  divided  ? 


XV. 

CORNELL  UNIVERSITY,  ITHACA,  N.Y. 

Entrance  Examination,  June,  1882. 

1.  Define :    an  abstract  number,    the   prime   factors   of  a 

number,  a  quotient,   a  mixed  number,    cube  root, 
percentage,  bank  discount,  compound  interest. 

2.  Get  the  sum  of  five,  five-tenths,  thirty-seven  thousandths, 

one-thousand    millionths,     XIX,    MDCCCLXXXI, 

o.is. 

3.  Find  all  the  common  divisors  of  225,  2025,  8100. 

4.  Divide  A  of  91  by  -^  of  637. 

5.  What  is  the  amount,  at  compound  interest,  of  $500  for 

2  years  6  months,  at  7  per  cent  ? 

6.  Get  the  square  root  of  530  to  three  decimal  places,  and 

give  the  reasons  for  the  several  steps  in  the  work. 

7.  Give  the  common  and  the  metric  tables  for  liquid  meas- 

ure ? 

8.  How  many  liters  in  10  gallons,  3  quarts,  1  pint,  3  gills, 

the  gallon  being  231  cubic  inches,  and  the   meter 
39.37  inches? 


86  EXAMINATION    PAPERS. 

XVI. 

STEVENS  INSTITUTE  OF  TECHNOLOGY,  HOBOKEN,  N.J. 

/Specimen  Entrance  Examination  Paper. 

1.  What  is  a  prime  number? 

2.  Find  the  L.G.M.  of  36,  48,  and  72.     Why  can  it  not  be 

found  by  first  dividing  by  36  ? 

3.  Find  the  G.C.D.  of  120,  228,  and  720. 

4.  If  John  sells  a  book  for  110  cents,  and  thereby  loses  12 

per  cent,  what  did  the  book  cost  him  ? 

5.  Find  the  square  root  of  0.4  to  three  places. 

6.  Find  the  cube  root  of  0.8. 

7.  Multiply  3  hundredths  by  300  -thousandths. 

8.  Divide  300  thousandths  by  3  hundred-thousandths. 

XVII. 

MADISON  UNIVERSITY,  HAMILTON,  N.Y. 

Entrance  Examination,  June,  1882. 

7      1515 

21  5  85  —  4  002 

1.  From  -  —  —  subtract  '——  -  -  -  ,  obtaining  the 


result  to  three  places  of  decimals. 

2.  Extract  the  square  root  of   102.002  to   two  places  of 

decimals. 

3.  What  is  the  interest  on  51584  for  1  year,  2  months,  and 

20  days  at  7  per  cent  ? 


ARITHMETIC.  87 


XVIII. 

VASSAR  COLLEGE,  POUGHKEEPSIE,  N.Y. 

Specimen  Examination  Paper  for  Admission. 

1.  Find  the  greatest  common  divisor  of  256,  480,  and  1296. 

2.  What  is  the  value  of  (^^-  +  16  ~ '8  -  |)  X  7TV  ? 

3.  What  is  the  sum  of  '»  °f^  and  f-^A? 


4.  Divide  two  thousand  five  hundred  one  and  four-tenths 

by  four  thousand  one  hundred  twenty-five  ten- 
millionths.  Divide  1.29136109  by  184.3,  and  write 
the  quotient  in  words. 

5.  A  gentleman  bought  a  yacht  for  $3500,  and  sold  it  at 

a  loss  of  20  per  cent ;  the  buyer  sold  it  at  a  gain  of 
25  per  cent ;  what  did  the  latter  receive  for  it  ? 

6.  What  sum  of  money,  at  10  per  cent  compound  interest, 

will  amount  to  $8651.50  in  three  years? 

7.  A  cistern  is  4m  long,  24dm  wide,  and  80cm  deep.     How 

much  water  will  it  hold  in  cubic  meters?    In  liters? 

8.  The  longitude  of  St.  Petersburg  is  39°  19'  east ;  of  New 

York  74° 41'  west;  when  it  is  one  o'clock  in  the 
afternoon  at  St.  Petersburg,  what  time  is  it  at  New 
York? 

9.  Extract  the  square  root  of  4.932841. 


88  EXAMINATION    PAPERS. 

XIX. 

COLLEGE  OF  NEW  JERSEY,  PRINCETON,  N.  J. 

Examination  for  Admission,  Sept.,  1883. 


2.  State  and  demonstrate  a  rule  for  finding  the  greatest 

common  divisor  of  any  set  of  integers  ;  and  make 
use  of  it  to  find  the  greatest  common  divisor  of 
847,  1331,  and  1573. 

3.  Prove  that  any  circulating  decimal  may  be  reduced  to 

a  rational  fraction.  To  what  fraction  is  the  circu- 
lating decimal  0.57  equal  ? 

4.  Two  bodies  let  fall  at  different  instants  from  the  same 

point  are  found,  \|-^    -  seconds  after  the  latter  of 

\  981 

them  started,  to  have  fallen,  the  one  25m,  the  other 
100m.  These  distances  being  to  one  another  as  the 
squares  of  the  times  during  which  the  bodies  have 
been  falling,  how  many  seconds  must  the  one  body 
have  started  before  the  other  ? 

5.  What  per  cent  is  3  of  6  ?    What  is  the  number  to  which 

if  2  per  cent  of  itself  be  added  the  sum  is  516  ? 

6.  The  amount  of  a  certain  principal  at  a  certain  rate  of 

interest  for  6  months  is  $949.76,  and  for  1  year  at 
the  same  rate  is  $1003.52.  Required  the  rate  per 
cent  and  principal. 

7.  The  dimensions  of  a  room  are,  length  4m  ldm,  breadth 

3m  2cm,  and  height  3m  lmm.  Find  its  cubical  contents 
(in  kilosteres)  and  the  area  of  its  walls  (in  centares), 


ARITHMETIC.  &9 


XX. 

JOHN  C.  GREEN  SCHOOL  OF  SCIENCE,  PRINCETON,  N.  J. 

Entrance  Examination,  Sept.,  1883. 

1.  Simplify  |±|f. 

2.  Find  the  G.O.M.  of  252,  315,  420,  and  504. 

3.  Find  the  square  root  of  0.434  to  three  decimals. 

4.  If  I  sell  goods  at  4  per  cent  commission,  and  receive 

$60,  what  amount  have  I  sold? 

5.  Find  the  edge  of  a  cubical  can  which  will  hold  27.57kg 

of  sulphuric  acid,  whose  specific  gravity  is  1.8. 

XXI. 

UNIVERSITY  OF  PENNSYLVANIA,  PHILADELPHIA,  PA. 
Examination  for  Admission,  June,  1882. 


i. 


n    a-      r*     5i-0.042-2. 

2.  Simplify      - 


3.  Simplify  0.6  of  3.3  +  -of  17+0.4  of  5.75- 

2-625  2.095238 

4.  Extract  the  square  root  of  5683  to  four  places  of  decimals. 

5.  A  rectangular  piece  of  ground  is  32m  7dm  long,  and  19™ 

5cm  broad.  Find  the  cost  of  enclosing  it  with  a  path 
lm  5dm  broad,  at  3  francs  5  centimes  a  square  meter. 
(i.)  Path  outside  of  the  ground  ;  (ii.)  path  part  of 
ground. 

6.  A  house  cost  $5000,  and  rents  for  $25  a  month,  with 

$25  to  pay  annually  for  repairs  and  $50  for  taxes  ; 
what  is  the  difference  in  the  income  from  this  and. 
from  the  same  money  invested  in  6  per  cent  stock 
at  96? 


90  EXAMINATION    TAPERS. 

XXII. 

UNIVERSITY  OF  MICHIGAN,  ANN  ARBOR,  MICH. 

Examination  for  Admission,  June,  1883. 

1.  Reduce  -  -  to  a  simple  fraction,  and  state  the  pro- 

(> 

cess  and  principles. 

2.  Reduce  2  years  5  months  12  days  to  years  and  decimals 

of  a  year. 

3.  Extract  the  square  root  of  0.4. 

4.  Give  the  denominations  used  in  linear  measure  in  the 

metric  system. 

5.  How  are  the  measures  of  capacity  and  of  weight  in  the 

metric  system  related  to  the  linear  measures  ? 

XXIII. 

LAKE  FOREST  UNIVERSITY,  LAKE  FOREST,  ILL. 
Entrance  Examination,  June,  1882. 

1.  Add  ten    thousand   and   one  millionth  ;    four  hundred 

thousandths ;     ninety-six    hundredths ;     forty -seven 
millions  sixty  thousand  and  eight  billionths. 

2.  Define  integer,  compound  number,  the  power  of  a  num- 

ber, a  fraction.     How  many  classes  of  fractions  ? 

3.  Find  the  interest  of  $375.75  for  4  years  5  months  and 

25  days,  at  4?  per  cent. 

4.  If  the  wages  of  72  men  for  5  days  is  $450,  how  many 

men  may  be  hired  for  12  days  for  $540? 

5.  A  can  build  a  wall  in  18f.  days,  B  in  3H  days;  how 

long  will  it  take  both  together  to  build  it  ? 


ARITHMETIC.  91 


6.  What  is  the  present  worth  of  $3471.50,  due  3  months 

and  9  days  hence,  at  7  per  cent  ? 

7.  What  is  the  interest  at  4J  per  cent  of  $360.45,  from 

July  4,  1873,  to  November  3, 1875,  allowing  a  credit 
of  $75,  paid  October  5,  1874? 

8.  Reduce    to    equivalent    fractions,    having   a   common 

denominator,  f  of  f ,  2f ,  5f ,  f  of  £  of  3 J. 

9.  On  what  principal  at  7  per  cent,  in  1  year  and  3  months, 

will  the  interest  be  $15.40? 

10.   Extract  the  cube  root  of  225,866,529. 


XXIV. 

EDUCATION  DEPARTMENT,  ONTARIO. 

Examination  for  Admission  to  High  Szhools,  June,  1883. 

1.  What  is  the  object  of  division  ?     Write  down  the  rela- 

tion connecting  the  divisor,  dividend,  quotient,  and 
remainder. 

Divide  one  hundred  and  eight  billion  four  hundred  and 
nineteen  million  seven  hundred  and  sixteen  thou- 
sand and  one,  by  eighteen  million  seven  hundred 
and  forty-eight  thousand  and  five. 

2.  Find,  by  "  casting  out  nines,"  whether  the  following  is 

correct:  349,751  X  28,637  =  10,015,819,397. 

Find  the  weight  of  500,000  bricks  at  4  pounds,  2  ounces 
each,  and  the  cost,  in  dollars  and  cents,  at  27s.  Qd. 
a  thousand,  allowing  4s.  2d.  to  make  a  dollar. 

3.  A  merchant  received  from  England  the  following  in- 

voice in  sterling : 


92  EXAMINATION    PAPERS. 

375  tons  iron  plates,  at  £8  15s.  Grf.  ;  107&  tons  bar 
iron,  at  £11  14s.  ;  10  tons  bulb  iron,  at  £10  10s.  ; 
17  tons  T  iron,  at  £15  10s.  ;  48  tons  steel,  at  £18 
7s.  6  d.  ;  15  tons  rivets,  at  £  11  1  s.  Find  the  amount 
of  this  invoice  in  Canadian  currency,  allowing  the 
shilling  sterling  to  be  equal  to  24-^  cents. 

4.    At  $1.75  per  rod,  what  will  it  cost  to  fence  a  piece  of 
land  63.5  rods  long,  and  27.75  rods  wide  ? 


5.  Simplify  1  -  1  +  J¥  -  drtv  +  THfcr  =  J  and 

5.81  —  2.5^  441 
of  32  of  0.45      3760* 

6.  Gunpowder  is  composed  of  nitre,  charcoal,  and  sulphur, 

in  the  proportion  of  15,  3,  and  2.  A  certain  quan- 
tity of  gunpowder  is  known  to  contain  20  cwt.  of 
charcoal  ;  find  its  wreight,  and  also  the  weight  of 
nitre  and  of  sulphur  it  contains. 

7.  Bought  360  gallons  of  wine  at  §2.60  a  gallon  ;  paid  for 

carriage,  §17.20,  and  for  duties,  $86.50.  If  -^  of  it 
be  lost  by  leakage,  at  what  price  must  the  remainder 
be  sold  to  gain  $50  on  the  whole  transaction? 

8.  Find  the  interest  on  a  note  for  $257.81,  dated  January 

3,  1883,  and  paid  April  6,  1883,  at  8  per  cent  per 
annum. 

9.  The  length  of  a  second's  pendulum  is  39.37079  inches  ; 

if  64  French  meters  are  equal  to  70  yards,  by  what 
decimal  of  an  inch  will  the  length  of  a  second's  pen- 
dulum differ  from  one  meter  ? 

10.    At  what  times  between  4  and  5  o'clock  are  the  hands 
of  a  clock  (i.)  coincident?  (ii.)  at  right  angles? 


ARITHMETIC.  93 


XXV. 

EDUCATION  DEPARTMENT,  ONTARIO. 
Examination  of  Third  Class  Teachers,  July,  1883. 

1.  Add  together  -f-  of  £13,  £  of  -^  of  f  of  £2  12s.,  and  £ 

'0f9rf. 
Reduce  13s.  4J  c?.  to  the  decimal  of  19s.  Gel. 

2.  Find  by  practice  the  value  of  8596  pounds,  at  £10  18s. 

*l\d.  each. 

3.  A  person  borrows  §500  on  April  10,  and  on  June  22 

pays  his  debt  with  $510.20.  At  what  rate  per  cent' 
per  annum  was  he  charged  interest? 

4.  A  man  having  a  certain  sum  of  money  to  invest  has  an 

opportunity  of  purchasing  7  per  cent  stock  at  95, 
but  delays  until  it  has  risen  to  110.  What  per  cent 
is  his  income  less  than  if  he  had  purchased  at  the 
fipst  price  ? 

5.  At  an  international  exhibition,  one  country  was  awarded 

5  gold,  9  silver,  and  11  bronze  medals;  and  an- 
other, 4  gold,  15  silver,  and  10  bronze.  Find  a 
ratio  of  values  for  such  medals  that  these  countries 
may  be  regarded  as  equally  fortunate. 

6.  In  a  box  there  is  a  certain  number  of- sovereigns,  three 

times  as  many  guineas,  and  twice  as  many  marks 
(13s.  4<f.)  as  guineas.  The  entire 'amount  in  the 
box  is  £815.  How  many  coins  of  each  kind  are 
there  ? 

7.  Find  when  first  after  2  o'clock  the  hour  and  minute 

hands  of  a  clock  make  an  angle  of  60  degrees  with 
.  each  other. 


94  EXAMINATION    PAPERS. 

8.  For  each  of  three  succeeding  months  the  population  of 

a  north-west  town  rose  50  per  cent ;  and  at  the  end 
of  the  third  month  was  2700.  What  was  the  popu- 
lation at  the  beginning  of  the  time  ? 

9.  Leap  year  is  omitted  once  in  every  century,   except 

those  centuries  whose  number  is  divisible  by  4. 
What  is  the  average  length  of  a  year  ? 

10.  A  cube  is  formed  of  a  certain  number  of  pounds  Avoir- 
dupois of  a  substance,  and  the  same  number  of 
pounds  Troy  of  the  same  substance.  What  propor- 
tion will  a  side  of  the  cube  bear  to  a  side  of  a  cube 
formed  of  the  same  number  of  pounds  as  before,  but 
all  Avoirdupois?  (175  pounds  Troy  =  144  pounds 
Avoirdupois.) 

XXVI. 

EDUCATION  DEPARTMENT,  ONTARIO. 

Examination  of  Second  Class  Teachers,  July,  1883. 

1.  Prove  that  l  of  f  =  ^V 

Simplify  (2-f-  of  3TV)-f  *-(H  of  1A)-(1|  of  4T  of  A)- 

2.  The  pendulum  of  one  clock  makes  24  beats  in  26  seconds ; 

that  of  another,  36  beats  in  40  seconds.  If  they 
start  at  the  same  time,  when  first  will  the  beats 
occur  together? 

3.  A  can  do  as  much  work  in  4  hours  as  B  in  6 ;  and  B  in 

3|-  as  C  in  5.  A  does  half  a  certain  piece  of  work 
in  12  hours;  in  what  time  can  it  be  finished  by  B 
and  C,  working  separately  equal  times,  and  C  suc- 
ceeding B  ? 

4.  A  note  for  $500,  made  March  9,  at  3  months,  is  dis- 

counted April  11,  at  8  per  cent.  What  is  received 
for  the  note  ?  (True  discount.) 


ARITHMETIC.  95 


5.  The  unclaimed  dividends  on  a  certain  amount  of  stock 

which  pays  6  per  cent  per  annum  amounted  in  3 
years  to  $1152.  The  stock  was  sold  at  a  discount 
of  12-1-  per  cent  On  its  par  value.  What  sum  was 
realized  ? 

6.  Teas  at  3s.  6c?.,  4s.,  and  6s.  a  pound,  are  mixed  to  pro- 

duce a  tea  worth  5s.  a  pound.  What  is  the  least 
integral  number  of  pounds  that  the  mixture  can 
contain  ? 

7.  A  man  buys  150  pounds  of  sugar,  and,  after  selling  100 

pounds,  finds  he  has  been  parting  with  it  at  a  loss 
of  5  per  cent.  At  what  rate  per  cent  advance  on 
the  cost  must  he  sell  the  remaining  50  pounds  that 
he  may  gain  10  per  cent  on  the  entire  transaction  ? 

8.  Ea'ch  member  of  a  pedestrian  club  walks  as  many  miles 

as  there  are  members  in  the  club,  and  the  expense 
of  the  trip  is  for  each  member  as  many  pence  per 
mile  as  there  are  members  in  the  club.  The  total 
expense  is  £50  13s.  lid.  How  many  members  are 
there  ? 

9.  The  hour,  minute,  and  second  hands  of  a  watch  are  on 

concentric  axes.  When  first  after  12  o'clock  will 
the  direction  of  the  second  hand,  produced  back- 
wards, bisect  the  angle  between  the  hour  and  the 
minute  hands  ? 

XXVII. 

EDUCATION  DEPARTMENT,  ONTARIO. 

Examination   of   Third  and  Second  Class   Teachers,    July,    1883.  — 
Mental  Arithmetic. 

1.    A   hall- way  is   90  inches  wide,   and   takes  25  square 
yards  of  oil-cloth  to  cover  it.     How  long  is  it  ? 


96  EXAMINATION    PAPERS. 

2.  A  gentleman  travels  from  Toronto   to    Montreal   and 

back.  He  goes  at  an  average  rate  of  33  miles  per 
hour,  and  returns  at  an  average  of  30  miles  per 
hour,  and  he  finds  that  he  occupied  one  hour  longer 
in  returning  than  in  going.  Find  the  distance  from 
Toronto  to  Montreal. 

3.  A  can  do  a  piece  of  work  in  7  days,  and  B  can  do  it  in 

8  days.  A  works  at  it  for  2£  clays,  and  B  works  at 
it  for  3  days.  C  then  finishes  it  in  3f  days.  In 
how  many  days  could  C  have  done  the  whole  wrork 
alone? 

4.  By  selling  an  article  for  §21  I  would  lose  12i  per  cent. 

At  what  should  I  sell  it  in  order  to  gain  12«}  per 
cent? 

5.  A  merchant  marked  his  goods  at  an  advance  of  GO  per 

cent  on  cost.  He  gave  one  of  his  customers  a  dis- 
count of  15  per  cent  off  the  marked  price.  What 
was  his  gain  on  §6.80  received  from  that  customer? 

6.  How  much  stock  must  I  sell  out  of  the  3  2  per  cents,  at 

84,  to  enable  me  to  buy  $7700  4  per  cent  stock,  the 
value  of  the  stock  being  proportional  to  the  divi- 
dends they  pay  ? 

XXVIII. 

EDUCATION  DEPARTMENT,  ONTARIO. 

Examination  of  First  Class   Teachers,  July,  1883. 

1.    Define   a  recurring    decimal,   and    classify  the    several 

kinds. 

Prove,  in  any  way,  a  rule  for  converting  a  mixed  circu- 
lating decimal  into  its  equivalent  vulgar  fraction, 
and  apply  your  rule  to  convert  0.1013257. 


ARITHMETIC.  97 


2.  Perform  the  operations  here  indicated,  employing  con- 

tracted multiplication  and  division,  and  retaining  6 

,    0.3372+0.03172      n  nnr 

decimals  throughout : ^ '-  0.0004675. 

0-140.00 

3.  In  the  expression,   "  6  per  cents  are  at  103,"   explain 

fully  what  is  meant. 

A  person  sells  a  certain  amount  of  5  per  cents  Tor  86, 
and  invests  in  the  6  per  cents  at  103,  and  by  so  do- 
ing changes  his  income  by  one  dollar.  Is  the  change 
an  increase  or  decrease  ?  How  much  stock  does  he 
sell? 

4.  A  man  buys  a  note,  drawn  for  2  years  at  6  per  cent 

interest,  and  which  is  now  6  months  old,  at  15  per 
cent  true  discount.  After  keeping  it  9  months,  and 
receiving  one  payment  of  interest,  he  sells  it  to  a  bank 
at  8  per  cent  bank  discount.  What  per  cent  does 
he  make  upon  his  money  while  invested  ? 

5.  A,  B,  and  C,  whose  rates  of  walking  are  3|,  4,  and  5 

miles  an  hour,  respectively,  walk  on  circular  tracks 
whose  circumferences  are  8,  10,  and  15  miles,  respec- 
tively, and  whose  centres  are  in  the  same  straight 
line.  At  the  same  instant  they  start  from  points 
on  this  line,. and  on  the  same  side  of  the  centres. 
Find  (i.)  when  first  they  will  be  all  on  this  line  at 
the  same  time ;  (ii.)  all  at  same  time  at  the  points 
from  which  they  started ;  (iii.)  whether  they  will 
ever  be  all  at  the  same  instant  at  points  on  opposite 
sides  of  the  circles  to  the  starting  points. 

6.  I  ead  is  11.4  times,  and  zinc  7.2  times,  as  heavy  as  water. 

If  3  pounds  of  lead  and  2  pounds  of  zinc  be  melted 
together,  compare  the  weight  of  the  alloy  with  that 
of  water. 


98  EXAMINATION    PAPERS. 

7.  A,  B,  and  C  start  at  the  same  time  and  from  the  same 

point,  to  travel  around  an  island  26  miles  in  circuit. 
A  goes  10  miles  and  B  4  miles  per  hour  in  the 
same  direction,  and  C  goes  5  miles  per  hour  in  the 
opposite  direction.  When  and  where  will  they  first 
be  all  together  again  ? 

Algebraical  symbols  will  be  allowed  in  the  three  fol- 
lowing questions : 

8.  It  is  required  to  make  a  hollow  leaden  cylinder,  open 

at  both  ends,  10  inches  long,  with  its  wall  1  inch 
thick,  and  which  is  to  weigh  25  pounds.  Find  its 
outside  diameter. 

9.  A  conical  vessel,  6  inches  deep  and  3  inches  across  the 

mouth,  is  filled  to  5  inches  with  water.  Find  the 
diameter  of  the  sphere  which,  when  dropped  into 
the  cylinder,  will  raise  the  water  so  as  just  to  fill 
the  vessel. 

10.  The  diagonals  of  a  quadrilateral  plane  figure  are  10 
and  12,  and  they  intersect  at  an  angle  of  60°.  Find 
the  area  of  the  figure. 


XXIX. 

COLLEGE  OF  OTTAWA,  OTTAWA,  CAN. 

Matriculation  Examination.     Session  1881-82. 

1.  What  is  the  exact  value  of  ^2f  +  f  of  ^  +  f)  -5- 

\  -7     i/ 

2.  The  sum  of  two  numbers  is  240;  their  L.C.M.  is  1728. 

What  are  the  numbers  ? 

3.  Define  discount,  and  find  the  discount  on  a  bill  of  £10, 

due  at  the  end  of  a  year,  at  10  per  cent. 


ARITHMETIC. 


4.  Find  the  simple  interest  of  $442,  at  4  per  cent,  for  5 

years ;  and  the  compound  interest  of  $500,  at  3  per 
cent,  for  2  years. 

5.  The  sea  covers  -J--J-  of  the  surface  of  the  globe.     The  area 

of  Asia  is  -^y1-  of  that  of  Europe,  whilst  the  area  of 
Africa  is  -2T2- ;  the  area  of  America  is  -y^ ;  and  the 
area  of  Oceania  is  -|T.  Africa  having  an  area  of 
11,630,400  square  miles,  find  the  area  of  all  the 
other  parts,  and  that  of  the  entire  globe. 

6.  Prove  that  the  product  of  71(71  +  l)(2n  +  l)  is  always 

divisible  by  6,  whatever  be  the  whole  number  n. 

XXX. 

COLLEGE  OF  OTTAWA,  OTTAWA,  CAN. 

Matriculation  Examination.     Session  1882-83. 

1.  A  man  has  3  farms  of  56,  72,  and  88  acres,  respectively, 

and  wishes  to  fence  them  into  the  largest  possible 
fields,  having  each  the  same  number  of  acres.  How 
many  acres  did  he  put  in  each  ? 

2.  A  grocer  has  a  4-pound,  5-pound,  6-pound,  and  a  12- 

pound  weight.  What  is  the  smallest  tub  of  butter 
that  he  can  weigh  by  each  without  a  remainder  ? 

3.  A  man  owning  ^-J-  of  a  ship  worth  $48,064  sold  ^  of  his 

share.  What  part  of  the  ship  did  he  sell  ?  "What 
part  does  he  still  own  ?  and  what  is  this  part  worth? 

4.  What  is  the  worth  of  a  silver  cup  weighing  10  ounces 

16  dwt.,  at  12-J-  cents  a  pennyweight? 

5.  The  longitude  of  Ottawa  is  75°  43'  22"  W.  of  Greenwich ; 

the  longitude  of  Washington  is  77°  3'  1".  What  is 
the  difference  in  time  between  Ottawa  and  Wash- 
ington ? 


100  EXAMINATION    PAPERS. 

6.  A  lad  at  the  age  of  14  received  a  legacy  of  $5000  ;  he 

then  lent  it  at  8  per  cent  simple  interest.  What  is 
his  legacy  worth  when  he  is  21  ? 

7.  Two  men  hire  a  pasture  for  $  50  ;  one  put  in  20  horses 

for  12  weeks,  the  other  25  horses  for  10  weeks. 
How  much  should  each  pay  ? 

8.  A  milkman  bought  40  gallons  of  new  milk,  at  16  cents 

a  gallon,  and  60  gallons  of  skimmed  milk,  at  8  cents 
a  gallon,  which  he  mixed  with  12  gallons  of  water, 
and  sold  the  whole  at  24  cents  a  gallon.  What  was 
his  profit  ? 


9.   Simplify  ,         x(3fx5*)-l7|, 

and  find  their  sum. 


XXXI. 

McGiLL  UNIVERSITY,  MONTREAL,  CAN. 

School  Examination,  June,  1883. 

1.  What  is  the  meaning  of  numeration?  notation?  addi- 

tion ?  subtraction  ?  multiplication.  ?  division  ?  Divide 
three  hundred  sixty  millions  nine  hundred  nineteen 
thousand  eight  hundred  fifty-six  by  eighty-three. 

2.  What  letters  are  used  in  Roman  notation,  and  how  are 

they  combined  to  express  numbers?  Change  9909 
into  Roman  notation. 

3.  What  is  the  difference  between  a  vulgar  and  a  decimal 

fraction  ?     Convert        --  into  a  decimal. 


4.  Multiply  2.604  by  1.234,  and  divide  the  result  by  0.004. 

5.  Find  the  value  of  21  acres  3  roods  12  poles,  at  $45  per 


acre. 


ARITHMETIC.  101 


6.  Find  the  L.C.M.  of  3,  5,  9,  12,  17,  and  20;  and  the 

G.C.M.  of  441  and  693. 

7.  Calculate  the  simple  interest  on  $580  from  May  16, 

1882,  to  October  8,  1883  (both  days  inclusive),  at  5 
per  cent  per  annum. 

8.  If  the  wages  of  12  men  for  8  days  of  8  hours  each  be 

$135,  what  will  be  the  wages  of  25  men  for  12  days 
of  10  hours  each  ? 

9.  Find  the  cost  of  planting  a  rectangular  field  measuring 

34  poles  2  yards  by  26  poles  3  yards,  at  $6.50  per 
square  pole,  leaving  a  path  4  feet  wide  all  round  the 
field. 

10.  If  25  pounds  of  tea,  at  60  cents  per  pound,  be  mixed 

with  30  pounds,  at  47  cents,  find  the  price  of  the 
mixture  per  pound  in  order  that  there  may  be  a 
profit  of  18  per  cent. 

11.  If  a  house  had  been  sold  for  $7992,  there  would  have 

been  a  gain  of  8  per  cent  on  outlay.  How  much  per 
cent  is  lost  or  gained  by  selling  it  for  $7511  ? 

12.  Find  the  distance  between  the  opposite  corners  of  a 

rectangular  floor  which  measures  8  feet  3  inches  by 
12  feet  6i  inches. 

XXXII. 

UNIVERSITY  OF  CAMBRIDGE,  ENG. 

Second  Previous  Examination,  Dec.,  1880.  — Time  allowed,  2%  hours. 

1.  Find  the  G.C.M.  of  2301  and  3717,  and  the  L.C.M.  of 

192,  204,  and  272. 

2.  Divide  3&  -  4J  +  IJf  by  If  +  5#  -  7^. 


102  EXAMINATION    PAPERS. 

3.  A  kiloliter  contains  35.32  cubic  feet,  and  a  gallon  con- 

tains 277.274  cubic  inches  ;  how  many  gallons  are 
there  in  a  kiloliter? 

4.  Add   together  -|  of  a  guinea   and  a  half,  0.855  of  a 

pound,  and  1T77  of  2f  of  If  of  18s. 


5.  Extract  to  three  places  of  decimals  the  square  roots  of 

G  and  0.287. 

6.  Find  as  recurring  decimals  the  square  of  0.4,  and  the 

square  root  of  O.G94. 

7.  Calculate  the  cost  of  paper  for  a  room  18  feet  long,  16 

feet  broad,  and  ,12  feet  high,  allowing  40  square 
feet  for  doors  and  windows,  the  price  of  the  paper 
being  2s.  4d.  per  piece  of  12  yards  long  and  21 
inches  broad. 

8.  A  Cambridge  Poor  Rate,  at  lie?,  in  the  pound,  is  made 

up  of  the  Union  Contribution,  5Jc/.  ;  the  Borough 
Rate,  4d.-  the  Asylum,  etc.,  l±d.  The  rate  on  a 
certain  property  aritounts  to  £100  8s.  5f/.  ;  how 
much  of  this  is  for  the  Borough  Rate,  and  at  what 
amount  is  the  property  assessed  ? 

9.  Find  the  difference  between  the  amount  of  £1205,  put 

out  for  2  years  at  5  per  cent  compound  interest,  and 
the  present  value  of  the  same  sum  due  2  years 
hence  at  5  per  cent  compound  interest. 

10.  The  11.45  Exeter  express  from  Paddington  stops  first 

at  Swinden,  77J  miles  distant,  at  1.12.  In  the  whole 
journey,  194  miles,  15  per  cent  of  the  time  is  ex- 
pended in  'stoppage,  etc.  '  At  what  time  is  the  train 
due  at  Exeter? 

11.  What  income  would  be  derived  from  investing  £9350 

in  5^-  per  cent  preference  stock-  at  137^-? 


ARITHMETIC.  103 


XXXIII. 

UNIVERSITY  OF  CAMBRIDGE,  ENG. 

Previous  Examination,  June,  1881. —  Time  allowed,  2}  hours. 

1.  Arrange  in  order  of  magnitude  the  fractions  J-,  •£$,  T7j, 

and  T9y- ;  and  find  the  difference  between  the  greatest 
and  least. 

2.  Simplify  t=-f  of  f^-j  of  f-=  |  of  585. 


3.  Find  a  decimal  which  shall  differ  from  -J-J  by  less  than 

TTuTFTF' 

Q.      rf    1.875  ,  3.5 
amplify  ---  x  _. 

Find  the  sum  of 

2.4,  0.313,  0.567,  7.056,  4.17,  and  0.4304122. 

4.  Calculate  the  value  of  \3  +  2  V2  correctly  to  two  places 

of  decimals. 

5.  Find  by  practice  the  value  of  a  nugget  of  gold  weigh- 

ing 3  pounds  11  ounces  18  pennyweights  4  grains 
at  £3  17s.  Qd.  per  ounce. 

6.  A  lawn-tennis  ground  is  half  as  long  again  as  it  is 

wide.  The  cost  of  levelling  at  9cZ.  per  square  yard 
is  £176  8s.  Oc?.  Find  the  cost  of  enclosing  it  with 
an  iron  railing  at  7s.  6cl.  per  yard. 

7.  A  sum  of  £650  is  due  from  A  to  B  on  a  certain  day, 

and  £495  12s.  6d.  is  also  due  7  months  later.  Show 
that,  reckoning  interest  at  5  per  cent,  if  A  pay  both 
debts  at  the  end  of  3  months,  neither  of  them  will 
lose. 


104  EXAMINATION    PAPERS. 

8.  Brussels  carpet  is  2  feet  wide,  costs  6s.  Qd.  a  yard,  and 

will  last  5  years.  Kidderminster  carpet  is  2-^  feet 
wide,  costs  5s.  a  yard,  and  will  last  3  years.  Which 
is  the  cheapest,  not  reckoning  interest  on  your  outlay? 

9.  Two  men  and  three  boys  can  level  and  turf  352  yards 

of  a  cricket-ground  in  4  days ;  and  three  men  and 
two  boys  can  complete  276  yards  in  3  days.  Com- 
pare the  rates  of  working  of  a  man  and  a  boy. 

10.  A  man  has  £7220  stock  in  the   3  per  cent  consols. 

When  they  are  at  102|-  he  sells,  and  invests  in  the 
2-J-  per  cents  at  90-J-.  Find  the  change  in  his  income. 
(Brokerage  is  J  per  cent.) 

11.  A  steel  rod,  1  foot  long  and  1  inch  square,  weighs  3-J- 

pounds,  and  will  just  support  50  tons.  What  is  the 
greatest  length  of  steel  wire  which,  when  hung  up 
by  one  end,  will  just  not  break  by  its  own  weight? 


XXXIV. 

UNIVERSITY  OF  CAMBRIDGE,  ENG. 

Second  Previous  Examination,  Dec.,  1881.  —  Time  allowed,  2}  hours. 


1-    Simplify 

(^  ~  i)       <    ~ 

2.  Find  the  difference  between  -§  of  31  acres  2  roods  27 

'  poles,  and  -J  of  18  acres  1  rood  0  poles. 

3.  Reduce  5  days  16  hours  to  the  decimal  of  a  week. 

,0.321x0.321-0.179x0.179 
Find  the  value  of  --  o.331_0.179  " 


ARITHMETIC.  105 


4.  Find  the  square  roots  of  27^  and  90,018.0009. 

A  Christmas  dole  is  given  to  the  inhabitants  of  certain 
almshouses,  consisting  of  as  many  shillings  to  each 
as  there  are  inhabitants.  The  sum  so  expended  is 
£9  16s.  Qd.  How  many  inhabitants  are  there? 

5.  At  what  rate  per  cent  will  the  simple  interest  on  £236 

6s.  8  d.  amount  to  £17  14s.  6d.  in  2J  years? 

6.  Find  the  present  worth  of  £  1250  Os.  2^d.  due  7  months 

hence  at  3^-  per  cent. 

7.  What  sum  of  money  must  be  invested  in  4-J-  per  cent 

stock  at  83J  to  bring  in  an  income  of  £  219  ?   (Brok- 
erage is  ^  per  cent.) 

8.  A  man  walking  18  miles  finds  that  in  1  hour  40  min- 

utes the  distance,  he  has  walked  is  -f-  of  the  remaining 
distance.     Find  his  rate  of  walking. 

9.  A  cubical  cistern,  open  at  the  top,  costs  15  guineas  to 

line   with   lead  at  Is.  9d.  per  square  foot.     How 
many  cubic  feet  will  it  contain  ? 

10.  A  man's  income  is  increased  by  £200  ;  but  the  income 
tax  being  reduced  from  6  d.  to  5  d.  in  the  pound,  he 
pays  the  same  amount  of  tax  as  before.  What  is 
his  income  ? 

XXXV. 

UNIVERSITY  OF  CAMBRIDGE,  ENG. 

Previous  Examination,  June,  1882.  —  Time  allowed,  2|  hours. 


1.    Keduce  |^||  to  a  decimal,  and  2.48027  to  a  vulgar 
fraction  in  its  lowest  terms. 


106  EXAMINATION    PAPERS. 

3.  Find  the  cost  of  7  cwt.  2  quarters  23  pounds  at  £11 

Is.  Sd.  per  cwt. 

4.  A  man  who  has  sold  tea  at  half-a-crown  per  pound, 

making  a  profit  of  25  per  cent,  lowers  his  price  so 
as  to  gain  only  2c?.  per  pound.  In  what  ratio  must 
his  weekly  sale  increase  that  he  may  make  twice  as 
much  as  before  ? 

5.  Find  the  amount  of  £325  IGs.  Sd.  in  3J  years  at  4£ 

per  cent  simple  interest. 

6.  If  a  bill  of  £932  2s.,  due  Dec.  19,  be  paid  June  6,  find 

the  true  discount  to  be  allowed,  reckoning  interest 
at  4  per  cent  per  annum. 

7.  The  amount  of  sunshine  recorded  in  Jersey  last  year, 

in  the  month  of  April,  was  33  per  cent  of  the  possi- 
ble amount ;  and  the  average  length  of  the  night  in 
that  month  is  10  hours  30  minutes.  Find  how 
many  hours  of  sunshine  there  were  in  the  month. 

8.  The  length  of  a  side  of  the  base  of  the  Great  Pyramid, 

which  is  square,  is  500  Egyptian  cubits  : 
(i.)    Find  the  area  covered  by  it  in  acres,  roods,  etc., 

knowing  that  an  Egyptian  cubit  is  equal  to  18.24 

English  inches, 
(ii.)    Find  the  height  of  the  Pyramid  in  cubits,  having 

given  that  the  height  of  a  model  of  the  Pyramid, 

the  area  of  whose  base  is  8  square  feet  73  square 

inches,  is  22.225  inches. 

9.  Which  is  the  more  profitable  stock  to  invest  in,  3  per 

cent  at  83£,  or  3^  per  cent  at  97? 

10.  Two  men  undertake  to  do  a  piece  of  work  for  1  guinea. 
One  could  do  it  alone  in  6  days,  the  other  in  7  days. 
With  the  assistance  of  a  boy  they  finish  it  in  3  days. 
How  should  the  money  be  divided? 


ARITHMETIC.  107 


XXXVI. 

UNIVERSITY  OF  OXFORD,  ENG. 

Local  Examination,  Junior  Candidates,  May,  1881. 
•  Time  allowed,  2  hours. 

Every  candidate  is  required  to  satisfy  the  examiners  in  the  first 
part  of  this  paper.  The  second  part  is  intended  for  those  candidates 
only  who  offer  mathematics  as  a  subject,  and  is  not  to  be  attempted 
by  any  until  they  have  done  all  they  can  do  of  the  first  part.  Atten- 
tion should  be  paid  to  spelling  and  hand-writing.  No  credit  will  be 
given  for  any  answer,  the  full  working  of  which  is  not  shown. 

I. 

1.  Express  in  words  90,999,090,009  ;  and  in  figures,  two 

thousand  millions  four  hundred  thousand  and  sixty. 

2.  Multiply  810,901  by  809,101 ;  and  1  ton  0  cwt.  0  quar- 

'ters  5  pounds  by  449. 

3.  Divide  25,600,160,001  by  159,601;    and   £183    12s. 

Hd.  by  58. 

4.  A  field  containing  18  acres  36  poles  is  divided  into 

allotments,  each  containing  1  rood  14  poles.     How 
many  of  them  are  there  ? 

5.  Reduce  28  quarters  5  bushels  1  peck  1  gallon  to  pints. 

6.  Simplify   f^  ~^- ;  and  divide  0.00036  by  0.006. 

T5"  *   '12 

7.  Express  2  yards  3  inches  as  the  fraction  of  1  mile  30 

perches. 

8.  If  it  cost  £9   5s.  4  d.  to  carpet  a  room  whose  floor  con- 

tains 278  square  feet,  how  many  square   feet  are 
there  in  one  which  can  be  carpeted  for  £12  4s.  8d.  ? 


108  EXAMINATION    PAPERS. 

II. 

9.    Find  the  simple  interest  on  £11,000  for  4.4  years  at 
3.15  per  cent. 

10.  The  external  length,  breadth,  and  depth  of  a  box  are 

6  feet  2  inches,  3  feet  8  inches,  and  2  feet,  respec- 
tively, and  it  is  made  of  wood  1  inch  thick.  Find 
the  quantity  used. 

11.  Two  pipes  running  together  can  fill  a  cistern  in  8 

minutes,  and  one  of  them  alone  can  fill  it  in  24 
minutes.  How  long  would  the  other  alone  take  ? 

12.  If  12  men,  working  8  hours  a  day,  do  -f  of  a  piece  of 

work  in  20  days,  how  many  days  will  15  men, 
working  10  hours  a  day,  take  to  do  -J  of  it  ? 

XXXVII. 

UNIVERSITY  OF  OXFORD,  ENG. 

Local  Examination,  Senior  Candidates,  May,  1881. —  Time  allowed, 
2  hours. 

No  credit  will  be  given  for  any  answer,  the  full  working  of  which 
is  not  shown. 

1.  How  many  times  is  £27  15s.  7f  d.  contained  in  £1356 

6s.  9d  ?  and  how  much  remains  over? 

2.  Multiply  1  acre  3  roods  7  poles  4  yards  by  17. 

3.  Add  together  3^,  &£-,  JJ,  and  1J  of  •&• 

4.  In  a  row  of  25  houses,  each  house  has   17  windows, 

each  window  4  panes,  and  each  pane  measures  18 
inches  by  9  inches.  What  will  be  the  cost  of  glaz- 
ing all  these  windows  at  6  d.  per  square  foot  ? 


ARITHMETIC.  109 


5.  Multiply  47.025  by  0.128;  divide  1.05  by  0.875;  and 

f  (1.005  +  0.201)  X  (1.005  -  0.201) 
find  the  value  of  L  1.005  x  0.201 

6.  Reduce   £5  17s.   *l\d.  to  the  decimal  of  £100;   and 

find  the  value  of  0.709  of  5  tons  3  cwts.  14  pounds. 

7.  Find  the  cost  of  227  tons  15  cwts.  21  pounds  at  £  12 

13s.  4e?.  per  ton. 

8.  Extract  the  square  root  of  36,180,225  and  of  0.000144. 

9.  Find  the  simple  interest  and  amount  of  £225  13s.  4c7. 

for  2J-  years  at  4f  per  cent  per  annum. 

10.  If  the  value  of  47  pounds  1  ounce  of  silver  be  £184 

16s.  -J-cf.,  what  is  the  value  of  84  pounds  9  ounces? 

11.  If  27  men  mow  a  field  of  90  acres  in  7  days,  working 

8  hours  a  day,  how  many  men  will  be  required  to 
mow  200  acres  in  16  days,  if  they  will  work  10 
hours  a  day  ? 

XXXVIII. 

UNIVERSITY  OF  OXFORD,  ENG. 

Local  Examination,  Junior  Candidates,  June,  1882.  —  Time  allowed, 
2  hours. 

Every  candidate  is  required  to  satisfy  the  examiners  in  the  first 
part  of  this  paper.  The  second  part  is  to  be  attempted  by  those  can- 
didates only  who  offer  mathematics  as  a  subject.  Attention  should 
bo  paid  to  spelling  and  handwriting.  No  credit  will  be  given  for 
any  answer,  the  full  working  of  which  is  not  shown. 

I. 

1.  Add  together  seventeen  hundred  and  seventy,  a  hun- 
dred and  seventy  thousand  and  seventy,  and 
seventeen  million  eight  hundred  and  twenty-nine 
thousand  ;  and  express  the  result  in  words. 


110  EXAMINATION    PAPERS. 

2.  Multiply  302,050  by  702,090  ;  and  4  days  22  hours  33 

minutes  49  seconds  by  401. 

3.  Out  of  a  salary  of  25  guineas  per  quarter,  how  much 

will  be  saved  in  a  year,  when  the  expenditure  is  at 
the  rate  of  5s.  3d  per  day? 

4.  Divide  40,301  acres  0  roods  38  rods  9  yards  by  251. 

5.  Find  the   number  of  quarters,  bushels,  etc.,  in  2559 

pints. 

6.  Find  the  value  of 

Gfr  of  it)  +  (II  ^  f i)  ;  and  of  A  cwt.  +  3  poun(L 

7.  Divide  4.00004  by  0.0011;  and  reduce  0.00126  to  a 

vulgar  fraction. 

8.  If  6-J-  tons  of  coal  cost  £6  15s.  5d,  what  will  be  the 

price  of  5  tons  3  cwts.  ? 

II. 

9.  If  5  men  and  9  boys  could  do  a  piece  of  work  in  17 

days,  in  how  many  days  would  9  men  and  12  boys 
do  it,  the  work  of  2  men  being  equal  to  that  of  3 

boys? 

10.  Find  the  simple  interest  on  £2970  16s.  8d  for  3  years 

73  days  at  £3  2s.  6  d.  per  cent. 

11.  A  man  buys  goods  which  he  sells  again  for  £11  18s. 

-J-d,  making  a  profit  of  16  per  cent;  what  is  the 
buying  price  ? 

12.  Pipes  A  and  B  can  fill  a  cistern  in  3  minutes  and  5 

minutes,  respectively,  and  C  can  empty  it  in  7-J 
minutes.  In  what  time  will  the  cistern  be  filled 
when  A,  B,  and  C  are  all  open  ? 


ARITHMETIC.  Ill 


XXXIX. 

UNIVERSITY  OF  OXFORD,  ENG. 

Local  Examination,  Senior  Candidates,  June,  1882.  —  Time  allowed, 
2  hours. 

No  credit  will  be  given  for  any   answer,  the  full  working  of 
which  is  not  shown. 

1.  Reduce  121  quarters  1  bushel  1  peck  to  quarts. 

2.  Into  how  many  allotments,  each  containing  2  roods  10 

perches,  can  a  rectangular  field  450  yards  long  and 
121  yards  be  divided  ? 

3.  Reduce  to  their  simplest  forms  the  fractional  expressions, 


_ 


6-* 

4.  Square  109.901  and  0.23. 

5.  Extract  the  square  root  of  35,445.5929. 

6.  Reduce  f|  of  £2  2s.  9<£  to  the  vulgar  fraction  of  £2 

2s.  l^d. ;  and  express  in  money  0.304375  of  £5. 

7.  Find  the  weight  of  a  quantity  of  metal  worth  £2  2s. 

9c?.,  having  given  that  2  tons  8  cwts.  3  quarters  12 
pounds  is  worth  £1. 

8.  How  much  is  gained  or  lost  per  cent  by  buying  a 

number  of  oranges  at  5  for  twopence,  and  selling 
half  of  them  at  two  a  penny  and  half  at  three  a 
penny  ? 

9.  Find  the  simple  interest  on  £7446  12s.  2-fd.  for  If 

years  at  4f-  per  cent. 

10.  During  365  days  6  hours  the  earth  makes  366^  revo- 
lutions about  its  axis.  How  long  will  it  take  in 
making  879  revolutions  ? 


112  EXAMINATION    PAPERS. 

11.  If  3  men  can  reap  8  acres  in  5  days,  working  8  hours 
a  day,  in  how  many  days  can  8  men,  working  12 
hours  a  day,  reap  192  acres? 


XL. 

UNIVERSITY  OF  OXFORD,  ENG. 

First  Examination  of  Women,  May,  1880.  —  Time  Allowed,  2  hours. 

1.  Forty-five  telegraph  posts,  placed  at  equal  distances, 

extend  a  mile  ;  how  far  apart  are  the  posts? 

2.  How  many  articles  at  £3  7s.  Qd.  each  are  worth  as 

much  as  324  articles  at  £1  12s.  Qd.  each? 

•    2597  ,  If 

3.  Snnphfy  — +  ^. 

4.  Divide  25.6  hy  16,  2.56  by  0.16,  and  0.09  by  0.04. 

5.  Find  the  value  of 

tV  7ard  +  *ttrP°le  +  TTBT  rood  +  inrfinr  acre ; 
also  of  0.00008544921875  of  a  ton,  and  0.1805  of  a 
guinea. 

6.  If  12  men  or  15  women  do  a  piece  of  work  in  252 

days,  in  what  time  can  11  men  and  2  women  do 
the  same  piece  of  work  ? 

7.  Find  the  cost  of  papering    a  room  11  yards  2   feet 

4  inches  long,  6  yards  2  feet  wide,  5  yards  2  feet 
6  inches  high,  with  paper  1  yard  4  inches  wide,  at 
3  d.  a  yard. 

8.  Sugar  is  bought  at  \\d.  a  pound,  and  sold  at  £18  13s. 

4d.  a  ton ;  find  the  gain  or  loss  per  cent. 

9.  Divide  a  sovereign  between  A,  B,  C,  so  that  A  may 

have  fourpence  more  than  B,  and  B  tenpence  more 
than  C. 


ARITHMETIC.  113 


10.  A  gives  a  fifth  of  a  cake  to  B,  and  then  a  quarter  of 

the  remainder  to  C,  and  then  a  third  of  what  still 
remains  to  D.  What  portions  of  the  cake  will  A,  B, 
C,  D  respectively  have  ? 

11.  Which  is  the  better  investment,  a  four  per  cent  stock 

at  120,  or  a  five  per  cent  stock  at  166|? 

XLI. 

UNIVERSITY  OF  OXFORD,  ENG. 

First  Examination  of  Women,  June,  1882.  —  Time  allowed,  2  hours. 

1.  How  many  coins,  each  weighing  15  dwts.  18  grains, 

can  be  made  out  of  16  pounds  10  ounces  7  dwts.  18 
grains  of  metal  ? 

rt     n.      ,.,,     24  of  5-j 

2.  Simplify 


3.  Keduce  6  cwts.  2  quarters  24  pounds  to  the  fraction 

of  a  ton;  and  hence  find  the  value  at  17s.  6d.  per 
ton. 

4.  If  turf  is  sold  in  pieces  30  inches  long  and  9  inches 

wide  at  £1  Os.   10 d.  per  100  pieces,  what  is  the 
price  per  square  yard  ? 

5.  Find  the  cost  of  1095  chests  of  tea  at  £7  17s.  7-Jd.  per 

chest. 

6.  Keduce   0.00544   to  a  vulgar   fraction   in   its   lowest 

terms;   multiply  0.544  by  0.125;    and  divide  27.6 
by  276  to  six  places  of  decimals. 

7.  Keduce  2|  of  4%d.  to  the  decimal  (i.)  of  half-a-crown, 

(ii.)  of  7  half-crowns. 

8.  If  165  bales  of  goods  cost  £431  4s.  8%d.t  what  will 

264  of  the  same  cost  ? 


11-1  EXAMINATION    PAPERS. 

9.    Find  the  simple  interest  on  £844  4s.  4d  for  3J-  years 
at  4J  per  cent. 

10.  The  material  for  a  dress  cost  7  guineas :  if  the  price  of 

the  material  chosen  had  been  25  per  cent  higher 
than  it  is,  and  half  as  much  again  had  been  used, 
by  how  much  would  the  cost  have  been  increased? 

11.  Divide  £3  2s.  6d.  between  three  persons  so  that  the 

first  shall  have  7s.  Qd.  more  than  the  second,  and 
the  second  5s.  more  than  the  third. 

12.  If  -Jg-  of  the  pupils  of  a  school  are  in  the  sixth  form,  ^ 

in  the  fifth,  ^  in  the  fourth,  and  96  in  the  lower 
forms,  what  is  the  whole  number  of  pupils  in  the 
school  ? 


XLII. 

UNIVERSITY  OF  OXFORD,  ENG. 

First  Examination  of  Women,  June,  1883.  —  Time  allowed,  2  hours. 
1.    Divide  436  acres  3  roods  3  yards  4  feet  72  inches  by  19. 


5  +  ^ 


2,   Simplify  1H  of  6J-7|  o 


3.  What  fraction  of  £2  19s.  %d.  is  £1  12s.  9 

If  the  larger  of  these  sums  is  the  value  of  12  penny- 
weights of  gold,  of  what  weight  of  gold  is  the  other 
the  value  ? 

4.  A  person,  purchasing  a  carpet  for  a  room  21  feet  long 

and  15  feet  9  inches  wide,  chooses  a  material  which 
is  j-  of  a  yard  wide,  and  the  pattern  of  which  is 


ARITHMETIC.  115 


complete  in  each  yard  of  length.  How  much  carpet 
must  he  buy  in  order  that  the  pattern  may  be  un- 
broken, if  the  strips  are  to  run  lengthwise  in  the 
room  ? 

5.  Find  the  cost  of  11  tons  3  cwts.  3  quarters  1G  pounds 

at  £3  12s.  lid.  per  cwt. 

6.  -Multiply  25.3125  by  2.56;  divide  G4S  by  0.0256;  and 

from  the  sum  of  2.6  and  3.583  subtract  5.05. 

7.  Eeduce   £5   18s.   IQi-d,  to  the  decimal  of  £25;  and 

find  the  value  of  0.025  of  £1  +  0.35  of  17s.  6  J.  +  0.2 


8.  If  the  food  of  11  persons  for  13  weeks  costs  £112  12s. 

3d.,  what  will  it  cost  to  feed  26  persons  for  11  weeks 
5  days? 

9.  At  what  rate  per  cent  per  annum  will  £40  10s.  be  the 

simple  interest  on  £432  for  2J  years. 

10.  A  grocer  buys  6  cwts.  of  tea  for  £70,  and  sells  41  cwts. 

at  2s.  6d.  per  pound.  At  what  price  per  pound 
must  he  sell  the  remainder  to  bring  his  profit  on  the 
whole  to  exactly  20  per  cent  ? 

11.  A  person,  who  had  2  sons  and  4  daughters,  left  an 

estate  of  2800  acres  to  be  divided  between  them  so 
that  each  son  might  have  twice  as  much  as  each 
daughter.  If  one  of  his  sons  has  a  family  of  4  sons 
and  '2  daughters,  and  leaves  his  share  to  be  divided 
in  the  same  manner,  how  many  acres  will  each  of 
his  daughters  inherit  ? 

12.  From  a  cask  of  wine,  worth  2s.  3d.  per  gallon,  a  sixth 

part  is  drawn  and  replaced  by  wine  worth  only  Is. 
3d.  per  gallon.  What  is  now  the  value  per  gallon 
of  the  wine  in  the  cask  ? 


HG  EXAMINATION    TAPERS. 

XLIII. 

SCIENCE  SCHOOLS  AND  CLASSES,  ENGLAND. 

Mathematics,  First  Stage,  May,  1880. 

Not  more  than  three  questions  are  to  be  answered.     The  num- 
ber of  marks  assigned  to  each  question  is  given  in  brackets. 

1.  Divide  285,651  by  77,  using  only  short  division.    Obtain 

the  remainder  correctly,  and  explain  briefly  how 
you  obtain  it.  [6.] 

2.  What  interest  per  cent  does  a  man  get  for  his  money  by 

investing  in  the  three  per  cents  at  90  ? 
How  much  must  he  invest  to  give  him  an  income  of 
£1153  a  year.  [6.] 

3.  Add  together  f  of  a  guinea,  ^J  of  a  half  crown,  l-^ 

shillings,  and  ^  of  a  penny,  and  reduce  the  whole 
to  a  decimal  fraction  of  a  pound.  [8.] 

4.  A  man  owns  three  bills,  of  which  one  could  be  paid  by 

a  certain  number  of  florins,  another  by  twice  that 
number  of  half  crowns,  and  the  third  by  six  times 
that  number  of  shillings.  The  bills  amount  in  all 
to  £  7  3  s.  0  d.  What  are  the  several  amounts  ? 

[12.] 

5.  Copper  weighs  550  pounds,  and  tin  462  pounds  to  the 

cubic  foot.  What  will  be  the  weight  of  a  cubic  foot 
of  a  mixture  of  6  parts  copper  to  5  parts  tin  ? 

[12.] 

6.  A  plate  of  metal  is  106.58  inches  long,  14.6  inches  wide, 

and  2  inches  thick.  Supposing  it  to  be  melted,  and 
cast  into  an  exact  cube,  what  would  be  the  edge  of 
the  cube?  [12.] 


ARITHMETIC.  117 


XLIV. 

SCIENCE  SCHOOLS  AND  CLASSES,  ENGLAND. 

Mathematics,  First  Stage,  May,  1881. 

Not  more  than  three  questions  are  to  be  answered.     The  number 
of  marks  assigned  to  each  question  is  given  in  brackets. 

1.  Make  out  a  bill  for  the  following : 

1  cwt.  of  indigo  at  14s.  Qd.  per  pound. 
1  ton  of  cloves  at  Is.  2d.  per  pound. 
5  cwt.  3  quarters  18  pounds  spelter  at  4J  d.  per  pound. 
7  cwt.  1  quarter  14  pounds  block  tin  at  £  64  per  ton. 
Subtract  10  per  cent  discount  for  cash.  [7.] 

2.  Divide  0.736  by  2.85,  and  2.85  by  0.0736,  in  each  case 

to  four  places  of  decimals,  and  find  the  product 
formed  by  multiplying  the  two  quotients  together. 

[7.] 

3.  Find  the  G.C.M.  and  L.G.M.  of  3024,  4752,  and  7488. 

[8.] 

4.  A  man  invests  £3600  in  3  per  cent  stock  at  90.     He 

sells  out  at  80,  and  lends  -|  of  his  money  at  4  per 
cent,  and  f  at  5  per  cent.  How  long  must  the  loan 
last,  so  that  when  he  re-invests  his  money  in  3  per 
cents  at  90,  his  gain  on  interest  (simple)  may  exactly 
equal  his  loss  upon  principal  ?  [12.] 

5.  The  sides  of  a  rectangle  are  16  feet  and  10  feet  long 

respectively.  Find,  to  four  places  of  decimals,  the 
length  of  the  diagonal  of  a  square  whose  area  equals 
that  of  the  rectangle.  [12.] 

6.  Seventy-five  per  cent  of  the  area  of  a  farm  is  arable  ;  of 

the  remainder  85  per  cent  is  pasture,  and  the  rest  is 
waste ;  the  area  of  the  waste  is  3  acres  0  roods  20 
poles.  What  is  the  area  of  the  farm?  [12. ] 


118  EXAMINATION    TAPERS. 

XLV. 

SCIENCE  SCHOOLS  AND  CLASSES,  ENGLAND. 

Mathematics,  First  Stage,  May,  1882. 

Not  more  than  three  questions  are  to  be  answered.     The  number 
of  marks  assigned  to  each  question  is  given  in  brackets. 

1.  The  cost  of  labor  in  producing  a  certain   article  was 

£18  19s.  lie?.  It  was  made  by  five  persons,  who 
severally  spent  2,  3,  4^-,  6,  and  8  days  upon  it.  How 
should  the  money  be  divided  among  them  ?  [6.] 

2.  Eeduce  to  their  lowest  terms  the  fractions 

|  of  0.0603  .  i  +  l  +  i 


3.  Arrange  Q  *  »  o»  Vl.81,  and  1.346  in  order  of   magni- 

tude, and  find  to  five  places  of  decimals  by  how 
much  the  sum  of  the  largest  and  smallest  of  these 
numbers  differs  from  twice  the  other  number.  [8.] 

4.  "What  is  discount?     How  is  it  commonly  calculated? 

If  a  sum  of  £  1000  becomes  due  three  months  hence, 
what  is  its  present  value  as  commonly  calculated, 
and  what  as  correctly  calculated,  interest  being 
reckoned  at  5  per  cent?  [10-] 

5.  Given  that  a  meter  equals  3.2809  feet;   find  how  many 

square  meters  there  are  in  1000  square  yards.    [10.] 

6.  A  cubic  foot  of  copper  weighs  560  pounds.     It  is  rolled 

into  a  square  bar  40  feet  long.  An  exact  cube  is 
cut  from  the  bar.  What  is  its  weight  to  four  deci- 
mals of  a  pound?  [12.] 


ARITHMETIC.  119 


XL  VI. 

SCIENCE  SCHOOLS  AND  CLASSES,  ENGLAND. 

Mathematics,  First  Stage,  May,  1883. 

Not  more  than  three  questions  are  to  be  answered.     The  number 
of  marks  assigned  to  each  question  is  given  in  brackets. 

1.  What  is  a  decimal  fraction  ?     What  is  a  recurring  deci- 

mal? Express  -^  as  a  recurring  decimal,  and 
0.0173535 as  a  vulgar  fraction.  [6.] 

2.  Show  that  the  square  root  of  0.37  exceeds  the  cube  r.oofc 

of  0.217  by  a  difference  which  very  nearly  equals 

rk-  [10.] 

3.  A  publisher  sells  books  to  a  retail  dealer  at  55.  a  copy, 

but  allows  25  copies  to  count  as  24 ;  if  the  retailer 
sells  each  of  the  25  copies  for  6s.  9  d.,  what  profit 
per  cent  does  he  make  ?  [8.]  . 

4.  In  building  a  wall,  22,500  bricks  are  used  at  £1  12s.  a 

thousand,  135  bushels  of  lime  at  Is.  ^.\d.  a  bushel, 
16-J  loads  of  sand  at  3s.  6d.  a  load;  the  labor  is 
reckoned  at  9  s.  6  d.  per  thousand  bricks  laid ;  and 
300  coping  stones  are  used  at  Is.  *I\d.  apiece,  in- 
cluding cost  of  laying.  Make  out  the  above  in  the 
form  of  a  bill,  and  find  the  amount  after  deducting 
7^-  per  cent  for  prompt  payment.  [8.] 

5.  The  capital  of  a  trading  company  consists  of  4000  A 

shares  of  £80  each  and  2000  B  shares  of  £25  each; 
in  dividing  the  profits,  5  per  cent  of  the  amount  of 
each  share  is  first  paid,  and  then  the  remainder,  if 
any,  is  divided  equally  amongst  the  shareholders. 
The  profits  of  the  undertaking  in  one  year  were 
£34,853  12s.  6-J-cZ.;  how  much  would  be  paid  to 
the  holder  of  an  A  share  and  how  much  to  the 
holder  of  a  B  share  ?  [10.] 


120  EXAMINATION    PAPERS. 

6.  An  imperial  gallon  is  277.274  cubic  inches ;  a  Win- 
chester bushel,  2150.42  cubic  inches ;  how  many 
Winchester  bushels  are  equal  to  100  imperial 
bushels?  [6.] 

XL  VII. 

CIVIL  SERVICE  OF  GREAT  BRITAIN. 

Open    Competitive   Examination  for   Out-Door    Officers    of   Customs, 
July,  1876.  —  Time  Allowed,  2%  Hours. 

1.  Add  together  4f ,  2-f,  if,  and  ^ 

2.  Subtract  3-J-}  from  5^-- 

3.  Multiply  together  5-J,  T<V,  T%,  and  2£ . 

4.  Divide  5f  by  if. 

5.  Add  together  0.00867,  1.92,  0.806,  and  143.9576. 

6.  Subtract  382.7043  from  400.1036. 

7.  Multiply  381.42  by  0.0065. 

8.  Divide  1522.038  by  0.372. 

9.  Express  f-  of  4s.  1  d.  as  the  decimal  of  5  guineas. 

10.  Add  together  f ,  if,  11T45,  and  if 

11.  Subtract  8f  from  9TV 

12.  Multiply  together  -J-f,  3-f-,  3-J,  and  if 

13.  Divide  4|£  by  10T4T. 

14.  Add  together  0.725  of  a  bushel  and  2.079  of  a  gallon, 

and  give  the  answer  in  pints  and  the  decimal  frac- 
tion of  a  pint. 

15.  Subtract   10.869  of  an  ounce  from  1.203  of  a  pound 

Troy. 


ARITHMETIC.  121 


16.  Multiply  905.8  by  87.06. 

17.  Divide  0.0054837  by  0.0135. 

18.  Eecluce  0.70596  of  3s.  11$ d.  to  farthings  and  the  deci- 

mal of  a  farthing. 

19.  Reduce  4  tons  2  cwt.  1  quarter  11  pounds  to  ounces. 

20.  If  2J  pounds  of  rice  cost  7  d.,  how  much  may  be  bought 

for  £6  17s.  Id.? 

21.  Find  (by  practice)  the  cost  of  455,436  articles  at  £2 

13s.  10$  d.  per  dozen. 

22.  In  what  time  will  £1225  amount  to  £1417  18s.  9c?. 

at  3  per  cent  per  annum  simple  interest  ? 

23.  In  8,476,321  inches,  how  many  miles,  furlongs,  poles, 

etc. 

24.  If  2$  acres  of  pasturage  can  support  5  oxen  for  3$ 

days,  how  many  would  be  required  to  support  26 
oxen  for  17-J  days? 

25.  Find  (by  practice)  the  value  of  5  quarters  2  bushels 

1  peck  of  wheat  at  £4  18s.  a  quarter. 

26.  Find  the  amount  of  £4750  in  3  three  years  at  5  per 

cent  per  annum,  compound  interest,  neglecting  frac- 
tions of  a  penny. 

XL  VIII. 

CIVIL  SERVICE  OF  GREAT  BRITAIN. 

Open   Competitive  Examination   for  Men  Clerkships   in   the   Lower 
Division  of  the  Civil  Service,  Nov.,  1876. — Time  allowed,  3  hours. 

1.  A  and  B  together  earn  £3  16s.  in  8  days,  A  and  C 
together  can  earn  £7  13s.  in  17  days,  and  B  and 
C  together  £12  15s.  in  30  days.  How  much  can 
they  severally  earn  alone  ? 


122  EXAMINATION    TAPERS. 

2.  Express  32,567,325  in  the  duodenary  scale. 

3.  A  merchant  selling  goods  at  a  certain  price  loses  5  per 

cent ;  but,  if  he  had  sold  them  for  £4  more,  he  would 
have  gained  3  per  cent.  What  did  the  goods  cost 
him? 

4.  Multiply  by  duodecimals  3  feet  2  inches  by  5  feet  7 

inches,  and  the  product  by  6  feet  8  inches.  What 
does  the  answer  become  when  expressed  in  cubic 
inches  and  the  decimal  fraction  of  a  cubic  inch  ? 

5.  Extract  the  square  root  of  109ff|,  and  find  the  side  of 

a  cube  containing  2,048,383  cubic  inches. 

6.  What  is  the  present  worth  of  £1801  11s.,  payable  6J 

years  hence,  at  5  per  cent  per  annum  ? 

7.  A  bill  upon   Amsterdam  is  bought  at  12  florins  per 

pound  sterling;  the  proceeds  purchase  at  Amster- 
dam bills  upon  Hamburg,  at  34J  florins  for  40  marks ; 
these  are  forwarded  to  Paris  and  sold  at  185  francs 
per  100  marks.  What  is  the  rate  of  exchange  be- 
tween London  and  Paris? 

8.  A  train  is  just  27  minutes  in  passing  through  the  Mont 

Cenis  Tunnel,  the  length  of  which  is  11,220  meters ; 
find  the  speed  of  the  train  in  miles  per  hour.  (One 
meter  equals  39.39  inches.) 

9.  In  Reaumur's  thermometer  the  freezing  point  is  zero, 

and  the  boiling  point  80° ;  in  Fahrenheit's  ther- 
mometer the  freezing  point  is  32°,  and  the  boiling 
point  212°.  What  will  Reaumur's  thermometer 
mark  when  Fahrenheit's  marks  47°,  and  what  will 
Fahrenheit's  mark  when  Reaumur's  marks  93°  ? 
10.  A  and  B  rent  a  pasture  for  £138  per  annum  ;  A  puts 
in  200  sheep  and  B  160,  but  at  the  end  of  six 
months  they  dispose  of  half  their  stock,  and  allow  0 
to  put  in  120 ;  what  should  A,  B,  and  C  pay  sever- 
ally towards  the  rent  at  the  year's  end  ? 


AEITHMETIC.  123 


11.  It  is  noticed  that  the  water  in  a  reservoir  38  feet  long 

and  26  feet  wide,  which  is  known  to  leak,  sinks  one 
inch  in  12  hours.  A  pipe  discharging  60  gallons 
per  minute  will  fill  the  reservoir  in  45  hours,  allow- 
ing for  the  leakage.  Find  within  an  inch  the  depth 
of  the  reservoir.  (A  cubic  foot  of  water  contains 
6.25  gallons.) 

12.  A  man  invests  £26,180  in  the  3  per  cents  at  931,  but 

after  a  time  sells  out  half  at  921,  ancl  invests  the 
proceeds  in  the  4  per  cents  at  97.  Find  to  a  penny 
the  difference  in  his  income. 

13.  Find  the  value  of  3.6  of  0.954  of  0.428571  of  2s.  3d. 

14.  A  watch  gains  1  minute  and  15  seconds  a  day.     It  is 

set  right  at  noon  on  the  12th  of  November.  What 
will  be  the  true  time  when  it  points  at  noon  on  the 
following  Christmas  day  ? 

15.  The  first  of  a  line  of   10  sentries,  standing  at  equal 

distances  from  each  other,  wishes  to  send  a  message 
of  20  words  to  the  last.  The  men  begin  to  walk 
at  the  same  instant,  and  walk  even  distances  right 
and  left  of  their  posts  alternately,  and  each  time 
they  meet  pass  on  5  words.  The  transmission  of 
the  message  occupies  48  minutes,  and  the  men  walk 
at  the  rate  of  3  miles  per  hour.  How  far  is  the 
first  man  from  the  last  ? 

XLIX. 

CIVIL  SERVICE  OF  GREAT  BRITAIN. 

Competitive   Examination  for  the   Excise,  Dec.,  1876.  —  Elementary 
Arithmetic.  —  Time  Allowed,  2}  hours. 

1.  In  372,483  ounces,  how  many  tons,  cwts.,  quarters,  etc. 

2.  If  cotton  is  shipped  at  4  guineas  a  cwt.,  what  is  the 

weight  of  a  bale  costing  £  21  9s.? 


124  EXAMINATION    PAPERS. 

3.  Find  (by  practice)  the  value  of  27  pounds  6  ounces  6 

dwts.  of  gold  dust  at  £3  10s.  6d.  an  ounce. 

4.  Find  the  simple  interest  on  £6250  for  18  years  at  2J 

per  cent  per  annum. 

5.  Add  together  5f ,  |f,  if  >  and  3i- 

6.  Subtract  9^  from  10TJ^. 

7.  Multiply  6^j-  by  ff 

8.  Divide  31$  by  Iff. 

9.  Add  together 

371.87001,  0.0031,  0.00631,  and  5786.44321. 

10.  Subtract  185.939131  from  186.847. 

11.  Multiply  323.211  by  0.20343. 

12.  Divide  343.5777  by  0.525  to  three  places  of  decimals. 

13.  What  fraction  of  a  sovereign  is  0.345  of  £1  4s.  ? 

14.  Reduce  3  quarters  7  bushels  1  gallon  to  pints. 

15.  The  market  price  of  wheat  being  £3  4s  per  quarter, 

what  will  be  the  value  of  11  bushels  and  3  pecks? 

16.  Find    (by  practice)   the   dividend  on  £3760    15s.  at 

17s.  Qd.  in  the  pound. 

17.  Find  the  amount  of  £4096  in  3  years  at  1J  per  cent 

compound  interest  (neglecting  fractions  of  a  penny). 

18.  Add  together  5|i,  £,  3o4T,  and  1^. 

19.  Subtract  -j^  from  T7^. 

20.  Multiply  together  5-^,  ^,  ff ,  and  1^. 

21.  Divide  |£  by  6|. 


ARITHMETIC.  125 


22.  Add    together    11.431,    0.00101,    243.734,    400,    and 

1.3743. 

23.  Subtract  876.315  from  1000.01. 

24.  Multiply  7.3406  by  0.00437. 

25.  Divide  0.003634  by  0.0632. 

26.  Find  the  value  of  0.0625  of  an  acre. 

27.  Reduce  1  mile  7  furlongs  5  perches  2J-  yards  to  inches. 

28.  If  49  men  can  empty  a  reservoir  in  65  days,  pumping 

8  hours  a  day,  how  many  hours  a  day  must   196 
men  pump  to  empty  it  in  26  days? 

29.  Find  (by  practice)  the  value  of  7719  articles  at  £1  7s. 

6d.  per  dozen. 

30.  At  what  rate  per  cent  will  £461  10s.  amount  to  £611 

9s.  in  13  years  at  simple  interest? 

31.  Add  together  f  ,  •&,  Iff,  and  |f 

32.  Subtract  12^-  from  15^.  . 

33.  Multiply  together  T7¥,  3^-,  l-fa,  and  ^. 

34.  Divide  5f  by 


35.  Add  together  .1.001  of  a  cwt.  and  0.039  of  a  quarter, 

and  give  the  answer  in  ounces  and  the  decimal  frac- 
tion of  an  ounce. 

36.  Subtract  0.335  of  a  gallon  from  12.51  of  a  quart,  and 

give  the  answer  in  pints  and  the  decimal  of  a  pint. 

37.  Multiply  0.003631  by  200.001. 

38.  Divide  28.028  by  4900. 

39.  Reduce  13s.  Qd.  to  the  decimal  of  £3. 


120  EXAMINATION    PAPERS. 

L. 

CIVIL  SERVICE  OF  GREAT  BRITAIN. 

Competitive  Examination  for  the  Excise,  Dec.,  1876.  —  Higher  Arith- 
metic.—  Time  allowed,  3  hours. 

1.  An  estate  is  divided  among  three  persons,  A,  B,  C,  so 

that  A  has  -f  of  the  whole,  and  B  has  twice  as  much 
as  C.  It  is  found  that  B  has  27  acres  more  than  C. 
How  large  is  the  estate  ? 

2.  2  cwts.  1  quarter  3  pounds  of  an  article  is  bought  for 

15s.,  and  17  pounds  is  sold  for  Is.  3d.  What  profit 
is  made  per  cent  ? 

3.  What  fraction  of  300  yards  is  1  furlong  2  poles  6  yards 

2  feet  ?     Express  the  answer  as  a  decimal. 
Express  as  a  fraction  of  an  acre  the  ground  taken  up 
by  a  path  3  feet  broad  round  a  house,  the  front  of 
which  is  57  feet,  and  side  37  feet  long. 

4.  Extract  the  square  root  of  30,789^^-,  and  the  cube 

root  of  2,326,203.125. 

5.  How  many  ounces  of  silver  are  there  in  a  piece  of 

plate  costing  £59  10s.,  the  price  of  silver  being 
0.255  of  £1  per  ounce,  and  the  cost  of  manufacture 
-J-  the  value  of  the  silver  used  ? 

6.  Explain  what  is  meant  by  the  L.C.M.  of  two  or  more 

numbers? 
Find  the  L.C.M.  of  3696,  286,  19,656. 

7.  Find  the  value  of  1.72  of  0.276  of  15. 

8.  How  much  must  a  man  invest  in  3-J-  per  cents  at  91 

in  order  to  receive  £  590  per  annum,  after  paying 
4  d.  in  the  pound  income  tax  ? 


ARITHMETIC.  127 


9.  The  difference  between 'the  discount  and  interest  on  a 
debt  due  a  year  and  a  quarter  hence,  at  4  per  cent, 
is  5s.  What  is  the  debt? 

10.  A  tradesman's  prices  are  12  per  cent  above  cost  price. 

If  he  allows  £1  6s.  3d.  discount  on  a  bill  of  £21, 
what  profit  does  he  make  per  cent  ? 

11.  A  man  rents  a  house  from  the  first  of  January  at  £142 

per  annum,  payable  half-yearly.  He  sublets  it  for 
£160  per  annum,  payable  quarterly.  Allowing 
simple  interest  at  4  per  cent,  what  will  he  make  by 
the  transaction  in-  3  years  ? 

12.  A  cistern  containing  600  gallons  measures  externally  7 

feet  in  length,  2  feet  1.1  inches  in  breadth,  and  5  feet 
6  inches  in  height.  The  sides  being  H  inches  thick, 
what  is  the  thickness  of  the  bottom  ?  (A  cube  foot 
of  water  contains  6-^-  gallons.) 

13.  The  map  of  a  country  is  drawn  on  the  scale  of  ^  of 

an   inch   to  a  mile.     What   area  on  the  map  will 
•    represent  a  lake  4000  acres  in  extent  ? 

14.  A  fast  train  leaves  a  place  A  for  another  place  B  at 

the  same  moment  that  a  slow  train  leaves  B  for  A. 
The  fast  train  takes  2  hours  on  the  journey,  and,  if 
the  slow  train  kept  its  time,  they  would  meet  at  a 
distance  from  B  equal  to  -|  the  whole  distance  from 
A  to  B.  Instead  of  this,  the  place  where  they  meet 
is  at  a  distance  from  B  equal  to  -J  the  distance  from 
A  to  B.  How  much  behind  time  will  the  slow 
train  be  when  it  arrives  at  A  ? 

15.  A  round  column  stands  on  a  cubic  pedestal  of  the  same 

material,  whose  edge  is  6  feet.  The  column  is  hol- 
low, the  external  and  internal  diameters  measuring 
5  feet  and  4  feet,  respectively.  If  the  weight  of  the 
column  be  the  same  as  that  of  the  pedestal,  what  is 
its  height  ? 


128  EXAMINATION   PAPERS. 

LI. 

CIVIL  SERVICE  OF  GREAT  BRITAIN. 

Open  Competitive  Examination  for  Clerkships  of  the  Superior  Class 
in  the  India  Office,  1879.  —  Elementary  Arithmetic.  —  Time  allowed, 
2j  hours. 

1.  Reduce  6  tons  3  cwts.  2  quarters  14  pounds  to  ounces. 

2.  What  must  be  given  for  a  piece  of  silver  weighing  73 

pounds  5  ounces  15  pennyweights,  at  the  rate  of  5s. 
9  d.  an  ounce  ? 

3.  Find  (by  practice)  the  value  of  1  ton  3  cwts.  1  quarter 

14  pounds  at  £3  10s.  per  ton. 

4.  Find  the  simple  interest  on  £840  15s.  for  6-|  years  at 

3  per  cent   per   annum  (neglecting  fractions  of  a 
penny). 

5.  Add  together  fj,  4J-,  |f,  and  1^. 

6.  Subtract  7f<T  from  12^. 

7.  Multiply  SA  by  2&. 

8.  Divide  3-^  by  2Jf 

9.  Add  together  3106.8157,  0.0624,  0.00441,  and  43.2875. 

10.  Subtract  84.937658  from  100.3062431. 

11.  Multiply  947.36  by  0.00423. 

12.  Divide  950.562  by  19.56  to  three  places  of  decimals. 

13.  Reduce  0.0016395  of  a  pound  Troy  to  grains  and  the 

decimal  of  a  grain. 

14.  Reduce  8,868,097  square  feet  to  acres,  roods,  perches, 

and  yards. 


ARITHMETIC.  129 


15.  If  10  men'  can  build  a  wall  65  feet  long  and  5  feet  high 

in  3^  days,  in  how  many  days  will  6  men  build  a 
wall  80  feet  long  and  4  feet  high  ? 

16.  Find  (by  practice)  the  dividend  on  £g236  10s.  at  4s. 

7  d.  in  the  pound. 

17.  Find  the  amount  of  £  7205  in  3  years  at  6  per  cent 

compound  interest  (neglecting  fractions  of  a  penny). 

18.  Add  together  -J-,  TV,  •&,  and  4i- 

19.  Subtract  1£  from  3^. 

20.  Multiply  together  -f ,  -f-,  If,  and  1-J. 

21.  Divide  10J-  by  1-^, 

22.  Add  together  16.41215,  9.376,  0.00403,  177.42,  and 

27.03067. 

23.  Subtract  17.2398  from  27.06. 

24.  Multiply  46.2375  by  0.00743. 

25.  Divide  92.3784  by  0.623  to  four  places  of  decimals. 

26.  Find  the  value  of  1.025  of  £1  13s.  4d. 

27.  In  406,395  pints  how  many  bushels,  pecks,  gallons, 

etc.? 

28.  If  the  6d.  loaf  weigh  4  pounds,  when  wheat  is  at  36s. 

a  quarter,  what    should  the  \d.  loaf  weigh  when 
wheat  is  at  48s.  a  quarter? 

29.  Find  (by  practice)  the  value  of  17  ounces   10  penny- 

weights 12  grains  at  £1  13s.  4d.  an  ounce. 

30.  At  what  rate  per  cent  will  £2100  amount  to  £5250  in 

3  years? 

31.  Add  together  5f ,  -3J-,  f ,  and  |f. 

32.  Subtract  8-J  from 


130  EXAMINATION    PAPERS. 

33.  Multiply  together  10-J-,  2£,  f  and  3^.  ' 

34.  Divide  10|-  by  13. 

35.  Add  together  3.062  of  a  day  and  1.5347  of  an  hour, 

and  give  the  answer  in  minutes  and  the  decimal 
fraction  of  a  minute  ? 

36.  Subtract  5.017  of  a  furlong  from  1.358  of  a  mile,  and 

give  the  answer  in  yards  and  the  decimal  fraction 
of  a  yard  ? 

37.  Multiply  34.0069  by  0.005006. 

38.  Divide  0.038452  by  0.1005  to  three  places  of  decimals. 

39.  Reduce  £1.00065  to  farthings  and  the  decimal  of  a 

farthing. 

LII. 

CIVIL  SERVICE  OF  GREAT  BRITAIN. 

Open  Competitive  Examination  for  Clerkships  of  the  Superior  Class  in 
the  India  Office,  1879.  —  Higher  Arithmetic.  —  Time  allowed,  3 
hours. 

1.  If  26  sheep  be  worth  5  oxen,  2  oxen  be  equal  in  value 

to  3  horses,  and  7  horses  can  be  purchased  for  91 
guineas,  find  the  value  of  1  sheep. 

2.  Simplify  the  following,  and  express  the  results  as  deci- 

mals : 
(i.)  (2-H)x(3- 

r-\  2J-  of  3      U  of  _ 

(1L'  3frf2  ~  4  of          2   "  2}  +  I 
(iii.)  0.16  -f-  0.0027. 

3.  Divide  987,654,321  by  3509,  and  0.00321  by  0.000011. 

Find  the  value  of  2.0136  of  £2  1  s.  3d. 

4.  Explain  what  is  meant  by  the  G.C.M.  and  the  L.C.M. 

of  several  arithmetical  quantities. 


ARITHMETIC.  131 


Find  the  G.G.M.  of  5049,  4301,  3553. 

The  driving-wheel  of  a  locomotive  engine  is  27|-  feet  in 
circumference,  and  the  fore-wheel  16  feet.  Two 
particular  spokes,  one  in  each  wheel,  are  observed 
pointing  vertically  upwards.  How  far  will  the 
engine  travel  before  the  same  two  spokes  are  again 
simultaneously  in  the  same  direction,  and  how  often 
will  this  happen  in  9  miles  ? 

5.  What  is  the  present  worth  of  £1866  16s.,  payable  2 

years  hence  at  3  per  cent  per  annum? 

6.  The  area  of  a  rectangular  piece  of  ground  is  87  acres 

1  rood  26  perches.  What  is  its  length,  its  breadth 
being  462.5  links? 

7.  A  block  of  granite  is  17.7  feet  broad,  9.4  thick ;  what 

length  must  be  cut  off  so  as  to  contain  554.6  cubic 
feet? 

8.  Find  the  square  root  of  1,874,161.    Extract  to  4  places 

of  decimals  the  cube  root  of  0.002. 

What  must  be  the  side  of  a  cubical  cistern  which  is  to 
contain  1000  gallons  of  water,  if  a  gallon  contains 
277.164  cubic  inches? 

9.  A  grocer  mixes  2  kinds  of  sugar  at  4d.  and  61  d.  per 

pound,  taking  3  pounds  of  the  first  to  2  of  the  sec- 
ond. At  what  price  per  pound  must  he  sell  the 
mixture  to  gain  a  profit  of  20  per  cent  ? 

10.  Divide  £144  10s.  among  3  persons  in  the  proportions 

of  0.3,  0.33,  and  0.3. 

11.  A  merchant  invests  half  of  a  sum  of  money  in  the  3  per 

cents  at  92,  and  the  other  half  in  the  3-^  per  cents 
at  98.  Which  is  the  better  investment?  If  he 
receives  £44  as  income,  what  is  the  amount  of  the 
sum? 


134  EXAMINATION    PAPERS. 

22.  A  ditch  has  to  be  made  360  feet  long,  10  feet  wide  at 

the  top  and  3  feet  wide  at  the  bottom,  the  angle  of 
the  slope  of  each  side  being  45°.  Find  the  number 
of  cubic  yards  to  be  excavated. 

23.  A  circular  pond  has  an  area  of  346|-  square  yards. 

Find  to  the  nearest  penny  the  cost  of  fencing  it 
round  at  4s.  6c?.  per  lineal  yard. 

24.  A  cubical  block  contains  1  cubic  yard,  2  cubic  feet, 

541  cubic  inches.  Find  the  cost  of  covering  the 
entire  surface  with  lead  at  Is.  C>d.  per  square  foot. 

25.  A  hemispherical  punch-bowl  is  5  feet  6  inches  round 

the  brim.  Supposing  it  to  be  half  full,  how  many 
persons  may  be  helped  from  ifc  in  hemispherical 
glasses  If  inches  in  diameter  ? 

LIV. 

CIVIL  SERVICE  OF  GREAT  BRITAIN. 

Open  Competitive  Examination  for  Admission  to  the  Royal  Indian 
Engineering  College,  July,  1880.  —  Time  Allowed,  3  hours. 

1.  Add  together  4fl,  7^,  If  |f  ,  and  l|f 

2.  Subtract  2-f$  from  3^. 

3.  Multiply  together  1^,  17|,  l^f,  1-^,  and  2^. 

4.  Divide  7-&  by 


5.  Add  together  17.429,  0.0173,  1156.8,  and  0.0001723. 

6.  Subtract  60.25738  from  356.17. 

7.  Multiply  7.18  by  0.0919. 

8.  Divide  331.8553  by  55.3. 

9.  Express  1  peck  1  gallon  3  quarts  as  the  decimal  of  a 

quarter. 


ARITHMETIC.  135 


10.  Add  together  |f ,  ^,  and 

11.  Subtract  19JL-  from  20^- 

12.  Multiply  together  2-J,  1-g^,  1^,  and  -^ 

13.  Divide  7{|  by  l|f . 

14.  Add  together  2.25  of  a  cwt.  and  5.76  of  an  ounce,  and 

give  the  answer  in  quarters  and  the  decimal  of 
a  quarter. 

15.  Subtract  18.75  dwts.  from  2.12875  pounds,  and  give 

the  answer  in  grains  arid  the  decimal  of  a  grain. 

16.  Multiply  42.317  by  10.075. 

17.  Divide  48  by  0.144. 

18.  Reduce  19.062  furlongs  to  inches  and  the  decimal  of 

an  inch. 

19.  A  steel  plate  is  11  feet  6  inches  5'  long,  3  feet  2  inches 

8'  wide,  and  1  inch  3'  thick.  Find,  by  duodecimals, 
the  number  of  cubic  feet,  cubic  inches,  etc.,  it  con- 
tains. 

20.  Two  circular  courts  measure  40  and  50  feet  in  diam- 

eter. The  paving  of  the  former  costs  £  74  16  s.  8  d. 
Find  the  cost  of  paving  the  latter  at  the  same  rate. 

21.  A  rectangular  room  has  its  length,  breadth,  and  height 

as  7,  6,  5,  respectively.  Its  walls  were  decorated  at 
a  cost  of  2s.  6d.  per  square  yard,  and  its  ceiling 
finished  at  the  same  rate.  The  bill  for  the  whole 
was  £86.  What  will  be  the  expense  of  covering 
the  floor  with  carpet  at  7  s.  per  square  yard  ? 

22.  Find  the  cost  of  constructing  a  hemispherical  dome  of 

stone,  the  internal  diameter  of  which  is  45  feet,  and 
,  uniform  thickness  18  inches,  at  4s.  \d.  per  cubic 
foot  of  masonry. 


136  EXAMINATION    PAPERS, 

23.  The  diameters  of  a  conical  frustum  of  marble  are  17^- 

and  10-|-  inches,  and  the  height  24  feet.  Find  its 
volume. 

24.  A  and  B  receive  1GOO  cabbages  to  plant,  but  of  these 

10  prove  worthless.  A  plants  5  while  B  plants  4, 
and  the  rows  are  equal.  After  some  hours  they 
have,  not  sufficient  between  them  to  complete  an- 
other row,  A  having  45  to  spare  and  B  6.  A  then 
finds  he  has  planted  three  rows  more  than  B.  How 
many  did  each  plant,  and  how  many  cabbages  in  a 
row? 

25.  A  fast  train,  travelling  at  the  rate  of  36  miles  per 

hour,  leaves  Dover  for  London,  79  miles  distant,  at 
8  A.M.,  and  is  shortly  after  followed  by  a  slow  train 
whose  speed  is  24  miles  per  hour.  The  former  train 
meets  at  8.45  the  express  from  London,  which  covers 
48  miles  in  the  hour ;  and  the  slower  train  from 
Dover  meets  the  express  12-|-  minutes  later.  Find 
at  what  time  the  express  leaves  London  and  the 
slow  train  Dover,  supposing  both  trains  to  travel 
uniformly  between  Dover  and  London. 


LV. 

CIVIL  SERVICE  OF  GREAT  BRITAIN. 

Competitive  Examination  of  Candidates  nominated  for  Appointments 
in  the  India  Forest  Department,  Jan.,  1880.  —  Elementary  Arith- 
metic. —  Time  allowed,  2%  hours. 

1.  Eeduce  4  tons  1  cwt.  11  pounds  to  ounces. 

2.  If  1  pound  2  ounces  5  pennyweights  of  gold  cost  £69 

9s.  4-|-<f.,  what  is  the  price  per  ounce? 


ARITHMETIC.  137 


3.  Find  (by  practice)  the  value  of.  2  cwts.  2  quarters  21 

pounds  at  £4  per  ton. 

4.  Find  the  simple  interest  on  £3650  for  8  years  at  3J 

per  cent  per  annum. 

5.  Add  together  f ,  f ,  J,  and  -fa. 

6.  Subtract  2ff  from  4^. 

7.  Multiply  5-J-  by  1£. 

8.  Divide  5^-  by  2J-. 

9.  Add  together  0.20765,  0.00631,  6758.13247,  and  5.973. 

10.  Subtract  39.984  from  400.29. 

11.  Multiply  62.093  by  2.568. 

12.  Divide  14.9455  by  35.5. 

13.  Keduce  0.325  of  10  cwts.  to  pounds. 

14.  Reduce  2  pounds  3  ounces  4  pennyweights  to  grains 

Troy. 

15.  If  3  acres  2  roods  of  land  cost  £375,  what  will  be  the 

value  of  4  acres  2  roods  29.  perches  ? 

16.  Find  (by  practice)  the  value  of  32,679  articles  at  £1 

11s.  Qd.  per  dozen? 

17.  Find  the  amount  of  £2930  in  3  years  at  2  per  cent  per 

annum  compound  interest. 

18.  Add  together  2f ,  -ft,  3  J,  and  f 

19.  Subtract  15-ff  from  20-^-. 

20.  Multiply  together  2} ,  4£,  5f ,  and  f 

21.  Divide  if  by  2|. 


138  EXAMINATION   PAPERS. 

22.  Add  together  0.61692,  243.734,  400,    67.45213,  and 

2.683. 

23.  Subtract  284.7654  from  321.07659. 

24.  Multiply  2.8456  by  0.00325. 

25.  Divide  85.5  by  0.00684. 

26.  Express  3s.  9d.  as  the  decimal  of  a  pound. 

27.  In   1,320,765  square  inches,   how  many  acres,  roods, 

perches,  etc.  ? 

28.  If  the  second  class  railway  fare  is  -f-  that  of  the  first, 

and  the  third  class  J  that  of  the  second,  and  a  first 
class  passenger  can  travel  125  miles  for  £1  11s.  3d., 
how  far  can  a  third  class  passenger  travel  for  8s.  4  d.  ? 

29.  Find  (by  practice)  the  dividend  £269  17s.  &d.  at  13s. 

10  d.  in  the  pound. 

30.  In  what  time  will  £1050  amount  to  £1548  Is.  IQ^d. 

at  5J  per  cent  per  annum  simple  interest  ? 

31.  Add  together  5||,  2f ,  ^  and  |f. 

32.  Subtract  9-^-  from  19^,. 

33.  Multiply  together  if,  2f ,  yfc,  and  1^. 

34.  Divide  4|  by  6f . 

35.  Add  together  0.32  of  a  pound  and  0.45  of  a  shilling, 

and  give  the  answer  in  pence  and  the  decimal  frac- 
tion of  a  penny. 

36.  Subtract  0.428  of  a  gallon  from  3  quarts  1.25  pints, 

and  give  the  answer  in  pints  and  the  decimal  of  a 
pint. 

37.  Multiply  0.07864  by  0.000973. 

38.  Divide  16.8951  by  28,300. 

39.  Express  3  furlongs  2  poles  as  the  decimal  of  2J  miles. 


ARITHMETIC.  139 


LVI. 

CIVIL  SERVICE  OF  GREAT  BRITAIN. 

Competitive  Examination  of  Candidates  Nominated  for  Appointments 
in  the  India  Forest  Department,  Jan.,  1880.  —  Higher  Arithmetic. — 
Time  Allowed,  2J  hours. 

1.  Find  the  square  root  of  64.55961801,  and  of  70|i|. 

2.  Resolve  2520,  2772,  and  30,888  into  their  prime  fac- 

tors, and  thence  deduce  their  L.C.M. 

3.  Find  the  value  of  ^4f  .-*-  ^Tju")  X  °'3^  X  °'2^   of 

11  shillings.          *  7   •   42  / 

4.  Divide  £3293  6s.  6d.  among  5  persons  in  the  propor- 

tion of  the  fractions  -|-,  ^,  ^,  ^,  and  ^-. 

5.  Multiply  (by  duodecimals)  4  feet  3  inches  7  parts  by 

2  feet  6  inches  3  parts,  and  the  product  by  8  feet  9 
inches.  What  does  the  answer  become  when  ex- 
pressed in  cubic  feet,  cubic  inches,  and  the  fraction 
of  a  cubic  inch  ? 

6.  Find  the  length  of  the  edge  of  a  cube  containing  12 

cubic  feet  1216  cubic  inches,  and  the  cost  of  cover- 
ing this  cube  with  copper  at  10|-  d.  per  superficial 
foot. 

7.  A  plot  of  land,  containing  4  acres  3  roods  20  perches, 

is  valued  in  1879  at  £1681  17s.  6d.,  being  15  per 
cent  more  than  it  was  estimated  to  be  worth  in 
1878.  What  was  the  estimated  value  per  acre  in 
1878. 

8.  A  man  has  £5000  of  stock  in  the  3  per  cents.     He 

sells  out  when  they  are  at  98,  and  invests  £2000  in 
India  stock  at  104,  paying  4  per  cent,  and  the  re- 
mainder in  railway  shares  at  87|-,  paying  5  per  cent. 
Find  to  a  penny  the  alteration  in  his  income. 


140  EXAMINATION   PAPEKS. 

9.  A  cistern,  measuring  inside  4  feet  9  inches  long,  3  feet 
G  inches  wide,  and  3  feet  deep,  is  filled  with  water. 
Find  approximately  the  number  of  gallons  it  con- 
tains, and  the  weight  of  water  on  a  square  inch  of 
the  bottom.  (A  cubic  foot  of  water  is  equal  to  6.25 
gallons,  and  weighs  62.321  pounds.) 

10.  A  sovereign  of  standard  gold  weighs  5.136  dwts.,  and 

a  shilling  of  standard  silver  weighs  -^Q-  of  a  pound 
Troy.  What  weight  of  standard  silver  is  equivalent 
in  value  to  5  ounces  of  standard  gold  ? 

11.  A  water-tank  can  be  filled  by  one  tap  in  3  hours,  and 

by  another  in  2  hours.  It  can  be  emptied  by  a 
third  tap  in  1  hour  24  minutes.  The  tank  being 
empty,  all  three  taps  are  opened  at  once.  Kequired 
the  time  of  filling  it  under  these  circumstances. 

12.  A  starts  to  walk  from  London  to  Croyclon,  a 'distance 

of  10  miles,  at  the  same  moment  that  B  leaves  Croy- 
don  for  London.  A  walks  at  the  rate  of  3  miles  an 
hour,  and  B  at  the  rate  of  2J  miles  an  hour;  but, 
soon  after  they  started,  A  met  with  an  accident 
which  caused  him  to  lose  15  minutes  on  the  road. 
At  what  distance  from  London  will  they  meet  ? 


YB    I  /44c5 


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